The win put the United States on top of Group B with six points, one ahead of gold medal-favourite Serbia with two preliminary stage matches to go.
The Americans, runners-up four years ago in Beijing, seized control of the match early, jumping out to a 7-0 lead early in the second quarter and cruising from there against an outclassed British team that only qualified for the tournament as the host nation.
"We definitely wanted to start this game off stronger because we saw their two previous games when they came out on fire in the first quarter, and once a team gets going and the crowd gets behind them, they start throwing up shots and everything starts going in," Azevedo said. "We wanted to play strong defence and make sure we got a lead at the beginning."
Azevedo took care of that, firing two long-range shots past Britain goalkeeper Ed Scott and then converting a penalty to make it 3-0 just four minutes into the game. After pushing the lead to 7-0, the U.S. relaxed.
The American captain got plenty of help, with fellow four-time Olympian Ryan Bailey scoring three goals and Shea Buckner adding two more.
"Tonight we kind of settled in and kind of let off the gas a little bit after going up," coach Terry Schroeder said. "But I think we're real happy, we're 3-0 for sure so it puts us in a good place in our bracket and sets up a good match with Serbia here in two days."
After Serbia, the U.S. wraps up the group stage against three-time defending champion Hungary on Monday.
Ryan Lucas can be reached on twitter at www.twitter.com/relucaszSuggest a correction