The visitors had to withstand tremendous pressure with former Boro midfielder James Morrison booting two goal-bound efforts off the line and keeper Scott Carson saving superbly from Gary O'Neil, Afonso Alves and Mido.
Mowbray's men grabbed the points when impressive substitute Ishmael Miller booted a half-cleared Jonathan Greening corner back into the box and Olsson bundled it past keeper Ross Turnbull.
• Mowbray: Carson England class
Miller had replaced another substitute, Sherjill Macdonald, at half-time and instilled more purpose in an Albion attack which until the break had relied too heavily upon Czech Roman Bednar.
The statistics had suggested Albion were up against it as they chased their first away win against a Boro team confident at home, and the afternoon started badly with a serious-looking injury to Do-Heon Kim.
The South Korean midfielder slipped unchallenged close to the halfway line and collapsed to the turf, with play being held up for five minutes as he was strapped to a stretcher and carried off.
But the visitors, despite a tentative-looking formation with five strung loosely across midfield, looked confident and the Czech striker just failed to connect with a deep cross from the right by Gianni Zuiverloon.
Albion's caution was perhaps understandable given their failure to break their away day duck while Boro were going in search of a record fifth consecutive home win stretching back to the last campaign.
Boro responded in the 14th minute when Stewart Downing found space on the left and crossed towards Mido, only for Olsson to react with a superb saving challenge in the box.
Then Brazilian Alves burst into the box in the 18th minute after playing a clever one-two with Mido and clattered a rising effort against the underside of the bar before it was hacked to safety.
Robert Koren tried a long-range effort that sailed harmlessly into Turnbull's hands before a dull game sprang into life in the 35th minute when Borja Valero dipped a shot just over the bar from long range.
Two minutes later Olsson rose highest in the Boro box to connect with a Greening corner and head goalwards only for Turnbull to superbly tip his effort against the post.
And moments later at the other end Alves found himself with a similar chance but his header was booted off the line in the first of Morrison's two goal-line clearances.
Boro pressed at the start of the second half but it was Albion who snatched the lead in the 53rd minute when the impressive Miller dipped the ball back across the box for Olsson to stab home.
Boro piled forward from the re-start, O'Neil's free-kick almost teeing up Alves at the far post, then David Wheater's powerful header from a Downing corner headed off the line by Morrison.
Boro came even closer in the 65th minute when Downing crossed from the left but Carson managed to save at point-blank range from Mido before Alves bundled the rebound wide.
And they must have begun to feel it was not going to be their day when Carson palmed away an O'Neil effort in the 75th minute before also getting down to save the follow-up from Mido.
O'Neil slammed a long-range effort over the bar and Downing somehow failed to connect when he slid in to meet Adam Johnson's cross behind the Albion defence with seven minutes left.
Wheater directed a close-range header straight at Carson and Miller should have wrapped it up for the visitors in the dying seconds when he burst clear on the counter-attack but dragged his shot inches wide.
Mowbray: Carson England classWest Brom boss Tony Mowbray is convinced keeper Scott Carson will fight to
regain his England place after his stunning performance clinched the Baggies'
first away win of the season.
Carson pulled off a series of super saves to deny Gary O'Neil, Afonso Alves and
Mido as his side clung onto Jonas Olsson's 53rd-minute strike in the face of
tremendous Middlesbrough pressure.
Carson is still struggling to live down his international howler against
Croatia in a Euro 2008 qualifier but Mowbray believes his current situation at
The Hawthorns will enable his confidence and ability to flood back.
Mowbray said: "His talent will get him back into the England team if that's
what his goal is. He's got a settled place to come to work every day and that
will give him the stability he needs.
"As a 21-year-old boy playing in a game like that (for England) and having
that unfortunate situation, it's a great credit to his character and personality
that he's producing performances like he did today.
"Scott made some great saves. He's a lovely lad, he's got no edges about him.
He's a big lad and he's agile and alert. He does the right thing at the right
time and I'm delighted he's between our sticks.''
Mowbray's joy at claiming his first away win of the season at the home of his
former club was tempered by a serious injury to Do-Heon Kim, who fell to the
ground unchallenged in the first minute and was stretchered off.
Mowbray added: "He needs to go and get a scan but our doctor thinks the
minimum is his medial knee ligaments, which is six weeks out. And it could be
worse than that.''
Mowbray admitted he was not entirely satisfied with his team's performance as
they failed to make the most of some first-half chances and were forced to rely
on a sterling performance from the over-worked defence.
Mowbray said: "We've been a lot better than that in most of the games this
season and not got as many points. But people aren't interested about that. All
they want to know is the score and we'll take 1-0.''
Dejected Boro boss Gareth Southgate was once again forced to reflect on woeful
finishing as his side failed to make the most of a series of clear chances to
turn the game in their favour.
Southgate said: "We've had more than enough chances to win the game, never
mind draw it. But we haven't, and we've got to learn quickly. We can't keep
saying we deserved something and coming away with nothing.
"It's a lesson we've got to take on board very quickly. Up to the penalty box
we've done an awful lot right with the ball, and going forward we've had enough
chances to win two games.''
Defeat shattered Southgate's hopes of claiming a fifth consecutive Barclays
Premier League home win and he added: "I'm a bit more than fed up but you just
have to roll your sleeves up and go again. It was one of those days.''
Middlesbrough 0 - 1 West Bromwich Albion
