The Cardinals improved to 8-1 and kept alive their hopes for a BCS bowl game.
Their lone loss this year came against Central Florida, which joins Houston as the only teams without a league loss in the American Athletic Conference. Louisville is 4-1 in league action.
A win for Louisville over Houston next week could bring about a three-way tie for the conference title.
Birdgewater completed 21-of-37 passes for 288 yards and his 28-yard touchdown throw to DeVante Parker in the second quarter gave Louisville a 14-3 lead.
The Cardinals opened the scoring when Charles Gaines ran a blocked punt back 7 yards for a touchdown with 6:23 left in the first period. They also produced a defensive touchdown on Terell Floyd's 17-yard interception return in the third period.
Connecticut quarterback Tim Boyle went 14-of-29 for 113 yards and threw three interceptions.
The Huskies remained winless in its eight games this season and is 0-4 in conference play.