The Gunners, who went into the game boasting their best ever start to the competition, remain just a point clear of champions Manchester United as Boro ended their 11-match winless run.
It also lifted them out of the bottom three and eased the pressure on manager Gareth Southgate.
The home side were rewarded for their incredible work rate with an early Stewart Downing penalty and a second-half strike from Tuncay Sanli, who may finally be the solution to the club's goalscoring problems.
• Southgate thrilled with confidence boost
Tomas Rosicky maintained Arsenal's record of scoring in every Premier League game this season with a stoppage-time consolation but it was more than they deserved.
The result capped a miserable two trips to the north-east in five days for the Gunners, for whom the absence of talismanic midfielder Cesc Fabregas and other key players is beginning to tell.
Although under almost incessant pressure, they were uncharacteristically sloppy in possession and will surely need their better players available for sterner tests to come.
The Boro game looked a formality on paper, against a side they had beaten nine times in the last 12 meetings, losing only once.
Gunners manager Arsene Wenger arguably did his best to soften up opposite number Southgate earlier in the week by including the Boro boss among his list of potential new England managers.
The tactic failed as Southgate's men began determined to emulate the high-intensity game that saw north-east neighbours Newcastle snatch a draw against the same opponents in midweek.
It paid off as early as the third minute when the recalled Gary O'Neil's ball sent Jeremie Aliadiere into the area and Kolo Toure clumsily brought down his former team-mate, who was going away from goal.
Referee Howard Webb rightly pointed to the spot and Downing applied just enough pace on his penalty to beat Manuel Almunia low to his left.
Arsenal were rattled but could have levelled when top scorer Emmanuel Adebayor was just beaten to Bacary Sagna's cross by the fist of rookie goalkeeper Ross Turnbull, who continued to deputise for the injured Mark Schwarzer.
Boro were pressing from front to back and it was hard to see how they could maintain such a frenetic pace.
They could have had a freakish second when William Gallas' attempted clearance cannoned off Aliadiere but straight to Almunia, while Fabio Rochemback fired over from long range.
Arsenal took until the 22nd minute to have a serious shot at goal, Rosicky scuffing wide from 18 yards.
The Gunners were being knocked off stride, demonstrated when Emmanuel Eboue looked set to free Adebayor in behind but the through ball hit the striker's heels.
Toure saw a free-kick blocked as he tried to make amends for the penalty, before Rochemback - who was popping up all over the place - volleyed over at the other end.
Adebayor then headed a flighted Eboue free-kick inches wide, which Turnbull seemed to have covered.
Downing's free-kick effort posed no threat to Almunia, who had to be more alert to clutch a fizzing cross from Tuncay.
The Turkish striker, rewarded for his first Boro goal last week with a start against Arsenal, then fluffed his lines looking to curl a left-footed shot into the far corner.
Boro, whose intensity had dipped a little, found a second wind to finish the half ahead.
Wenger wasted no time shaking up his misfiring Gunners, bringing on Nicklas Bendtner for the disappointing Eduardo da Silva.
Arsenal had scored in every Premier League game this season, so it was not quite panic stations from the manager.
But it might have been five minutes after the restart when Rochemback capped a thrilling run with the perfect through ball to Tuncay.
With only Almunia to beat, the Turk's cross-shot screwed agonisingly wide of the far post.
Gael Clichy was booked for a late tackle on O'Neil before David Wheater saw a vicious goal-bound volley blocked.
Arsenal were conceding too many free-kicks and becoming frustrated with their inability to dictate the play.
Indeed, Boro were even beginning to out-pass them, the move of the match seeing Tuncay release Downing.
His cross was met first time by George Boateng 20 yards out but the captain's well-struck finish was just wide.
Wenger had seen enough, throwing on Denilson for Lassana Diarra and Theo Walcott for Eboue.
With the visitors committing more men forward, Bendtner mishit one over the bar and Adebayor got in behind only to see his cutback intercepted.
The danger for Arsenal was leaving themselves exposed at the back and almost as soon as Robert Huth was brought on for Jonathan Woodgate 17 minutes from time, Boro scored again.
A corner was not cleared properly and O'Neil's first-time shot was too hot for Almunia, whose parry was powered into the roof of the net by Tuncay, via a slight nick off Gallas.
Boro had the points in the bag long before Rosicky turned in Clichy's cross deep into stoppage-time.
Southgate thrilled with confidence boostVictory eased the pressure on Boro boss Gareth Southgate, who hailed the
result as the best of his 18 months in the job.
'It's the best result that we've had because of the manner of the win,' he
said.
Southgate revealed his masterplan for upsetting the Gunners, saying: 'Arsenal
have had a period of away games.
'I saw what Newcastle did the other night - I went up there.
'We needed to make sure from the first minute they were going to get exactly
the same again and we did that,
'We wanted to be on the front foot against them both in how we attacked and
how we defended.
'Because they're a class side and if you allow them time to play, they'll
destroy you.
'I felt it was a good afternoon to play them, with people like Fabregas and
(Alexander) Hleb missing, and we wanted to make the most of that opportunity.'
Downing's penalty handed Boro the lead for only the third time in the Premier
League this season and Southgate added: 'It's what we've been waiting for.
'It always a chicken-and-egg situation. We're not scoring and it's putting
pressure on the defence.
'Both aspects of the team have had to be better and they were today.
'The concentration levels were good. We caused them a lot of problems.'
Arsene Wenger admitted Middlesbrough fully deserved to end Arsenal's unbeaten
start to the Premier League season this afternoon.
'We lost the game because we deserved to lose it,' said a magnanimous
Wenger.
'It's that simple. Middlesbrough were sharper in the fight.
'We missed the start of the game by giving them too much room and it cost a
penalty.
'From then on, it was down to us being a little bit jaded physically. 'It
was our fourth away trip on the trot.
'We gave absolutely everything to come back. We lacked creativity, sharpness
in our passing so therefore we were not dangerous enough to come back into the
game.'
Wenger said he would watch the penalty award again before deciding whether it
was correct.
It looked like a good call from Howard Webb after Kolo Toure's clumsy
challenge felled former Gunners team-mate Jeremie Aliadiere.
'It gave them a lot of courage,' Wenger said of the incident.
'In fairness, they defended well, Credit to them, they were sharper than us
and you could see, once we were 1-0 down, if we do not come back before
half-time, it will be difficult.'
Indeed, not only did a below-par Arsenal fail to equalise, they fell further
behind 17 minutes from time when Tuncay lashed in on the rebound after Manuel
Almunia could only parry Gary O'Neil's shot.
Boro's victory owed everything to hard work, denying their opponents time and
space and Wenger offered reluctant praise for their efforts. 'They were good at
taking the space every time they won the ball back,' he said.
'Players like (Fabio) Rochemback, they know when to foul you.
'They played a cup game today.'
On the evidence of the past week, it appears Wenger is beginning to miss
talismanic midfielder Cesc Fabregas and other creative players.
Wenger said: 'At the moment we miss many in the same area. Maybe it handicaps
a bit our creative potential.'
Middlesbrough 2 - 1 Arsenal
