On defense, Dwight Dobbins and Dexter McCoil intercepted North Texas' Andrew McNulty, playing in place of injured starter Derek Thompson, and returned both for scores.
It was the first home victory for Tulsa (2-3) coach Bill Blankenship, whose team's three losses have come against national powerhouses Oklahoma, Boise State and Oklahoma State.
"There are no little (losses) and no little (wins)," Blankenship said. "They are all big (wins). This was an important win for us. These guys beat Indiana last week, and Indiana just played Penn State to within one touchdown.
"We got off to a fast start on both sides of the ball. Those pick-sixes really help."
McNulty was 11 for 18 for 158 yards and directed a scoring drive early in the fourth quarter, capped by Lance Dunbar's 7-yard run. Dunbar ran for 127 yards on 40 carries. Sophomore quarterback Brent Osborn threw two late touchdowns to Dunbar and Ivan Delgado for the Mean Green (1-4).
Tulsa finished with 412 yards of total offense despite having the ball for just over 19 minutes of the game. Kinne, who is still recovering from a knee injury suffered two weeks ago, said the Golden Hurricane made the most of its limited opportunities.
"It was weird and kind of hard to get into a rhythm because we were on the bench so long," Kinne said. "But it was good to get back to scoring fast and playing Tulsa football."
McCoil weaved 74 yards for a score after intercepting McNulty on Tulsa's first possession of the second half to make it 34-3. Carter barreled in from 2 yards out to make it 41-3 after three quarters.
"Tulsa played tonight like the team we thought they were," said North Texas coach Dan McCarney. "They haven't held themselves back this year; it's been the competition. They played three of the top five teams in America. They are really good and are going to win a lot of games, but we made their jobs easier with some of the mistakes we made."