Giggs, at 38 years and 243 days, became the oldest man to appear in the Olympic football competition and then became the oldest scorer when he headed Britain in front after 16 minutes.
The result, Britain's first win in the Olympics since they beat Taiwan 3-2 in the Rome Games in September 1960, put them top of Group A with four points having scored more goals than Senegal who stunned Uruguay 2-0 earlier at Wembley.
"We certainly made hard work for ourselves but all credit to the UAE," coach Stuart Pearce told reporters.
"The two substitutes had a real impact and we had some really good performances from the likes of Craig Bellamy and Joe Allen."
Pearce reserved his highest praise for Giggs, enthusing: "Ryan brings respect. That's a word that's used cheaply nowadays but the way he handles himself on and off the pitch is outstanding and we are delighted he got a goal this evening."
Britain will now qualify for the last eight of their first Olympics for 52 years as long as they do not lose to Uruguay in Cardiff next Wednesday while the UAE are eliminated after losing their first two games.
DOMINANT BRITAIN
The game was full of entertaining football with Britain dominating much of the play in front of a crowd of 85,137 - the biggest to ever watch a British Olympic match - until the UAE came back with Rashed Eisa equalising after 69 minutes.
They deserved their goal too with Eisa, Ismael Matar and Ahmed Khalil playing some neat penetrative football in midfield and attack.
After recovering from the shock of conceding, Britain rallied with two goals in four minutes from Sinclair, who scored with his first touch after 73 minutes, and Sturridge who added the third with a brilliant chip over goalkeeper Ali Khaseif in the 76th minute.
"It was a fantastic ball from Tom Cleverley," said Sturridge, who suffered a bout of viral meningitis before the Games started which threatened his place in the side.
"I took it across the keeper and just looked for a cheeky chip and it worked out for me."
The performance was the best of the three matches the team has played since the squad came together three weeks ago.
Following a 2-0 warm-up defeat to gold medal favourites Brazil and last Thursday's 1-1 draw with Senegal in their Group A opener at Old Trafford, Britain looked far more assured and played more like a team than before.
Pearce shuffled his defence around and gave Giggs a free role in midfield and he relished the opportunity, evoking memories of his younger self when he started the move with a jinking run that led to his goal.
His cross to his Welsh compatriot Craig Bellamy was returned perfectly and he rose to meet Bellamy's ball to head home.
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