The home side dominated the first half but only had Ryan Giggs's headed goal to show for their efforts as goalkeeper Ali Khaseif Housani and the woodwork kept Stuart Pearce's men at bay.
A turgid second half was sparked into life on the hour mark when Rashed Eisa Alfalasi exploited a gap in the home defence to strike a cool finish past Jack Butland.
Mahdi Redha's team created a few chances as Britain flagged, but the introduction of Scott Sinclair on 72 minutes reaped instant rewards when he tapped in from close range after Housani failed to hold a low cross from the excellent Craig Bellamy.
Daniel Sturridge, who came on for Marvin Sordell at half-time, chipped in a classy third to cool the home fans' nerves.
Team GB go top of Group A on goals scored, ahead of Senegal who shocked Uruguay with a 2-0 win earlier on Sunday.
A draw in their final match against Uruguay would guarantee progress to the quarter-finals, although a defeat would probably see Britain exit.
Things started well for Britain, who conceded a late equaliser against Senegal in their opening match on Thursday.
With Sordell preferred to Sturridge, who only recently recovered from meningitis, the home side went on the offensive from kick off as the Bolton forward’s low ball flashed across the face of goal but just beyond Aaron Ramsey.
The hosts took the lead just after the quarter-hour mark as Giggs went on a driving run, finding Manchester United team-mate Tom Cleverley before Bellamy’s fine cross picked out the Welsh veteran, whose late run was capped off by a bullet header.
Sordell made Housani work with a nice touch and shot from the edge of the box, but he was otherwise disappointing as a poor first touch constantly let him down.
Bellamy, a livewire as always, forced the keeper into action with an angled drive, with Housani making his best save of the day at the feet of Cleverley, who was sent one-on-one by Ramsey.
Cleverley thought he had scored just before half time as a fine run and cut-back from Bellamy was met with a cool finish that hit the inside of both posts before bouncing to safety.
It appeared to be a bad omen for the Brits when, 15 minutes into a disappointing second half, Alfalasi exploited poor positioning from a sluggish James Tomkins to run clean through before beating the onrushing Butland with a low finish.
That goal shell-shocked the Brits, who were all at sea for around 10 minutes, Butland making the save of the game from Omar Adulrahman after a lovely passing move from a now confident UAE.
The Arabian side were enjoying themselves a little too much for Pearce’s liking and, while eyebrows were raised when he took off the tiring Giggs for the electric Sinclair, the England U21 boss saw his decision vindicated within seconds.
The good work again came from Bellamy, who was aiming for Sturridge with a vicious low cross, while Housani blotted his copybook by palming the ball into the path of the Swansea winger, who made no mistake with the goal at his mercy.
Natural order was restored two minutes later, Sturridge chipping the onrushing Housani after a Xavi-esque through-ball from Cleverley, and at 3-1 there was no way back for the UAE, who exit the tournament with their heads held high after some memorable moments against more established nations.
Pearce was happy his tactical changes made the crucial difference for his side at a time when the result was in the balance.
“I would say probably the substitution from the manager was the real turning point – the two subs came off the bench and made a real impact for us, which was pleasing,” he said.
“Certainly the result was the most important thing this evening – we needed to win this game to give us a lift and enhance the belief in the group.
“There were some good parts but there are still things to work on. We won’t go away thinking it was a bed of roses.
“There were some real solid performances, certainly from Craig Bellamy and Giggs and Joe Allen and Tom Cleverley.”
The win leaves Team GB knowing a point or better against Uruguay will be enough to qualify for the quarter-finals, but Pearce confirmed his side will go for the win.
“We have to build for the last game against Uruguay – they need to beat us and we need to beat them,” he said. “We are going to try and win every game – we’ve set the team up to do that always.
“I think we can improve on the performance from tonight. We always expected we would improve on the performance game by game and it’s going to be a tough one but we have got to recover and get ready for it.”