Johnson, who grew up in suburban New Orleans, had 252 all-purpose yards, including a crushing 66-yard punt return for a touchdown in the fourth quarter, and Tulsa beat Tulane 37-13 in the season opener for both teams on Friday night.
Kinne, who sat out 2008 after transferring from Texas, passed for 211 yards, including a 12-yard touchdown pass to Trae Johnson, and also rushed for 77 yards, including a 15-yard touchdown.
Damaris Johnson had played in the Louisiana Superdome before, winning a state championship with current LSU quarterback Jordan Jefferson when the two played for Destrehan High School. Against Tulane, with family in the stands, he had 85 punt return yards, 76 kickoff return yards, 60 yards receiving and 31 yards rushing.
None of that came as a great surprise. Johnson set a Tulsa record for kickoff return yards last season with 1,382 and led Conference USA in all-purpose yards with 2,475.
Tulane starter Joe Kemp was 16-of-26 passing for 278 yards, one interception and a 20-yard touchdown pass to Casey Robottom, but his slow start helped Tulsa put the Green Wave in an early 17-0 hole.
Tulane was unable to get more than one first down in its first two offensive series and Kemp was sacked three times, ensuring good field position for the Hurricane's wide-open, no-huddle attack.
Tulsa's first drive started on the 50-yard line and was highlighted by Damaris Johnson's 28-yard run, which set up Kevin Fitzpatrick's 22-yard field goal to make it 3-0.
Tulsa's second drive started on the Tulane 42 and lasted only four plays before Kinne froze Tulane's defense with a fake handoff and ran to his right for a score.
Soon after, Kemp's tipped pass was intercepted by linebacker Mike Bryan and returned 18 yards to the Tulane 5. Charles Clay scored from 5 yards out on the next play to make it 17-0. Bryan was credited with 11 tackles in the game, including a forced fumble.
Tulane had chances to make it closer, but managed only one field goal on three drives inside Tulsa's 15-yard line. Ross Thevenot's first field goal attempted was kicked low and blocked by Odrick Ray.
Thevenot later connected from 27 yards to make it 17-3 late in the second quarter, but Johnson's 39-yard kickoff return gave the Hurricane the ball at its own 46 with 45 seconds left, and Tulsa drove for Fitzpatrick's 33-yard field goal as time expired to make it 20-3 at halftime.
Tulane squandered another chance to score after Jeremy Williams broke two tackles on a short reception and broke free for a 68-yard gain to the Tulsa 4. Tulane then ran the ball four straight times and turned the ball over on downs.
Williams had 139 yards receiving in all and had a spectacular touchdown catch between two defenders called back for a holding penalty.
Tulane got as close as 23-10 on Robottom's touchdown catch in the third quarter, but Johnson's punt return gave the momentum back to Tulsa for good.