McGee, a product of Texas A&M, came in early in the exhibition opener for Dallas and completed 14-of 24 passes for two touchdowns and 208 yards.
Dwayne Harris caught a 76-yard scoring throw from McGee early in the fourth period to tie the game, but Denver took the lead on an 8-yard scoring pass from Brady Quinn to Eron Riley with 5:44 left.
McGee then drove the Cowboys 65 yards and brought them within a point when he hit a diving Harris with a 13-yard touchdown throw on fourth down with 15 seconds to go. Rather than have an overtime, Dallas went for two extra points, which McGee converted on a scramble by hitting Martin Rucker in the end zone.
Tim Tebow started at quarterback for the Broncos and 6-of-7 passes for 91 yards. Kyle Orton, currently listed as No. 1 on the depth chart, was 2-of-6 for 37 yards.
Dallas starter Tony Romo was 3-of-5 for 33 yards in one series of work.