Hasselbaink appeared to be at least two yards ahead of the advancing Justin Hoyte when he collected a long punt upfield by Hermann Hreidarsson - but play was waved on as the assistant kept his flag down.
A simple cutback to Darren Bent at the far post left the England man clear to touch in his fifth goal of the season.
Arsenal were incensed, with manager Arsene Wenger leading the protests on the touchline - but television replays showed it to be a marginal call at the time the ball was humped forwards.
In the 32nd minute Alexander Hleb again had space to turn inside the box, and chipped the ball back over to the awaiting van Persie, who made no mistake in despatching a low drive into the bottom-right corner.
And the visitors took the lead when Emmanuel Eboue crossed the ball along the edge of the penalty area.
Van Persie had timed his run to perfection - and leapt to rocket a stunning left-foot volley into the roof of the net, before celebrating with Gunners fans behind the goal.
Thierry Henry wasted a chance before setting up van Persie in the six-yard box, but the striker touched the ball wide with the goal - and a hat-trick - beckoning.
Charlton had what looked strong appeals for a handball and a penalty against William Gallas turned away following Bent's overhead kick, before Hasselbaink flashed a close-range header wide from Bryan Hughes' cross.
Wenger hails Van Persie strike
Arsenal manager Arsene Wenger described Robin van Persie's brilliant winner at
Charlton as a 'goal of a lifetime'.
The Dutch forward, 23, struck once in each half after the Addicks had taken
the lead through Darren Bent on 21 minutes.
It was his second effort just following the restart which was a worthy
contender for goal of the season, as Van Persie leapt to volley a fantastic
18-yard strike into the top corner.
Wenger declared: 'It was quite unbelievable - a goal of a lifetime. Nobody
expected that.
'I did not see anybody in the box and then suddenly Van Persie arrives.
Technically it was perfect, with full pace and power.
'I felt the ball would go over the bar at the start, then suddenly it
finished in the top corner.'
Van Persie had been cautioned just before equalising on 32 minutes, and Wenger
revealed he had considered taking the Dutchman out of the firing line.
Wenger - who this week celebrated 10 years at Arsenal - said of Van Persie:
'Just after the incident, I waited a bit to see how he responded to it.
'That is football - if I had substituted him, people would have said yes I
did the right thing, if he got sent off after people would have said I was
stupid.
'That shows that as a manager you need luck as well because I kept him on and
he scored two goals.'
It is now five straight wins for Wenger's men in all competitions.
The Arsenal boss said: 'Charlton fought very hard and when you go away after
a Champions League game and are 1-0 down, you need some quality to win.
'It was an entertaining game.
'We could have finished it off a few times, but Charlton could also have come
back with a few minutes to go and the header from [Jimmy-Floyd] Hasselbaink.
When I saw it was him, I thought it was 2-2.'
Wenger added: 'My team is very hungry.
'To come here, be 1-0 down and then get back, up the tempo and win, that
tells you a lot about the hunger of this group.'
The Arsenal boss, however, admitted he could now do without the forthcoming
international break.
Wenger said: 'We have maintained the momentum, with five games on the trot,
but the negative thing is the interruption.
'When the players come back, they do not have the same focus on the club as
they did before they went away.
'Then the Champions League match [in Moscow] comes straight after the
international week.'
For Addicks boss Iain Dowie, it was another case of the result not matching
the effort put in by his injury-hit side.
Charlton have now lost six out of their seven Barclays Premiership matches,
and find themselves in deep trouble at the wrong end of the table.
Dowie, though, remains ever positive.
'The effort and the commitment were excellent, as were the fans too because
they have seen the team have a real go,' reflected the Addicks manager.
'No-one likes to lose six from seven, I am smarting from it and the lads
should be.
'But the players deserve no criticism, if anyone does, it is down to me.
'It is just disappointing not to get a result when our football second half
deserves that.'
Charlton had a strong shout for a penalty when William Gallas appeared to
handle an overhead kick from Bent during the closing stages.
Dowie reflected: 'All you want is for the referee to say: `Yeah, I got it
wrong.'
'If he does, then I have no issue with that - but I am not going to hold my
breath expecting a call from Mark [Clattenburg].'
The Charlton manager also felt Van Persie could have been shown a red card for
his challenge on Hasselbaink, which resulted in a caution just before he
scored.
'If you kick someone off the ball, then it is a sending-off - and there is no
ball there,' said Dowie.
'It is a very difficult job, refereeing.
'But is that more blatant than Gary Neville at Reading? Is it a handball for
Bolton today?
'They are influencing games.
'My issue is, okay I accept that - as long as you have an honest reply and
say, `I got it wrong'.'
Of Van Persie's fine second goal, the Charlton boss added: 'On another day
you would have liked to have been at home applauding it.
'It is supreme technique.'
Charlton Athletic 1 - 2 Arsenal
