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."
"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."
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.
His cross to his Welsh compatriot Craig Bellamy was returned perfectly and he rose to meet Bellamy's ball to head home.
