Tulsa (3-1) amassed 517 yards of total offense against the outmanned Bearkats (1-2) of the Southland Conference.
Kinne completed 12 of 15, including touchdown tosses of 30 yards to Slick Shelley, 63 yards to Damaris Johnson and 16 and 34 yards to Trae Johnson.
Kinne, who also led Tulsa in rushing with 58 yards on five carries, found the pickings easy compared with his struggles the previous week in a 45-0 loss at Oklahoma. He played one series in the third quarter, leading Tulsa to another score without throwing a pass. The key play was a 16-yard run by kicker Kevin Fitzpatrick on a fake field goal. Wide receiver A.J. Whitmore scored on a 5-yard run, culminated by a leap over the left pylon.
Reserve quarterback Jacob Bower rumbled 15 yards for a score, freshman tailback Willie Carter ran 39 yards for another and Charles Opeseyitan scored from 2 yards out.
Tulsa scored on five of its first six possessions in building a 35-3 halftime lead and led 56-3 with 2:57 to go in the third quarter.
Damaris Johnson led Tulsa's receivers with three catches for 103 yards. The sophomore went over the 1,000-yard mark for his career and surpassed 100 yards for the fourth time.
Tulsa, which led the nation in total offense the previous two years, surpassed 50 points and 500 yards for the first time in 2009.
It was the third impressive defensive outing in four games for Tulsa. The Hurricane has allowed 13 or fewer points to every opponent except Oklahoma. The Bearkats had averaged 38 points and 497 yards per game.
Sam Houston State moved the ball effectively early but managed just a field goal by Miguel Antonio. Quarterback Blake Joseph completed 7 of 18 passes for 87 yards. Sam Houston State managed just 241 yards of total offense and lost two fumbles.