O'Brien threw for a career-high 420 yards and three touchdowns and Jackson had nine catches for a career-high 214 yards and two touchdowns.
Dane Wright added 105 yards receiving for the Rams (2-5, 1-2 Mountain West), who ended a four-game losing streak.
Bryson Carroll had 193 yards rushing for the Lobos (2-3, 0-2), who lost a third straight game.
The Rams jumped out to the early lead on a 42-yard touchdown catch by Trey McBride, but New Mexico scored the next two touchdowns, one coming after Carroll went 56 yards before dropping the ball untouched on the 1-yard line.
Colorado State responded with Jackson's 87-yard touchdown reception, then Marvin Kinsey, who rushed for 85 yards and two TDs, scored his first touchdown five seconds before halftime.
The Rams took a step forward toward achieving bowl eligibility, but they have little room for error, particularly with improving Wyoming and No. 14 Boise State looming as the season's final two games.
The Lobos' slide takes them to the bottom of the conference's Mountain Division and now they hit the difficult portion of the schedule as all six upcoming opponents are above .500.
Colorado State next pays at Fresno State on Oct. 26.
New Mexico is at Wyoming on Oct. 19.
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College football bowl projections
There are still big games left on the schedule, but see how our experts envision the entire bowl season playing out.