Jamison scored the first points of the game on his long run up the middle with 9:42 left in the second quarter, weaving his way through the Tulane defense.
Tulane managed one sustained drive, settling for a 32-yard field goal at the start of the fourth quarter to pull within 10-6 after moving 69 yards in 17 plays. The next time Tulane had the ball, Jones stepped in front of a pass at the Green Wave 14 and scored easily.
Rutgers tacked on a 43-yard touchdown pass midway through the fourth quarter to make the score 24-6.
Tulane lost its 11th consecutive game dating to last year, its longest losing streak since dropping 16 in a row from 1961-63.
It was the head-coaching debuts for Rutgers' Kyle Flood, who replaced current Tampa Bay Buccaneers coach Greg Schiano in January, and Tulane's Curtis Johnson.
Flood was Schiano's assistant head coach the past four seasons before Schiano left for the NFL after 11 years at Rutgers.
Jamison rushed for 112 yards on 18 carries, adding 41 yards on two receptions. Nova struggled for most of the night before his touchdown pass, finishing 11 of 20 for 158 yards.
The Rutgers defense, which returned eight starters after ranking 14th nationally in yards allowed, held Tulane to 262 yards and kept the Green Wave out of the end zone until late in the fourth quarter. Tulane had minus-5 yards rushing in the first half and finished with 8 yards on the ground.
Tulane's Ryan Griffin completed a career-high 34 passes in 48 attempts, but he also was sacked three times and pressured constantly. He threw his only touchdown pass to running back Robert Kelley when the Green Wave trailed 24-6 and the game was out of reach.
Tulane's Ryan Grant led all receivers with six catches for 110 yards.
Rutgers' offense struggled to move consistently, but the Scarlet Knights relied on big plays. That included a 55-yard kickoff return by Jeremy Deering in the final minute of the first half, setting up a 28-yard field goal as time ran out to make the score 10-3.