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.
Pollack: Utah is better than Oregon
David Pollack and Jesse Palmer debate if Utah has a better chance of making the College Football Playoff than Oregon.
College Football Playoff rankings: What the games would look like today
Here's what the College Football Playoff and New Year's Six bowl games would look like based on Tuesday's rankings.
LSU, Ohio State, Clemson and Georgia remain at the top
Rece Davis reveals the top 6 in this week's College Football Playoff rankings with LSU, Ohio State, Clemson and Georgia remaining in the playoff.
Sooners inching closer to the top
Rece Davis reveals 25-7 in this week's College Football Rankings, including the Oklahoma Sooners moving another spot closer to the top 6.
LSU atop CFP again; Alabama stays at No. 5
The rest of the top four remains the same as last week: No. 2 Ohio State, No. 3 Clemson and No. 4 Georgia.
Franklin: Death threats aimed at PSU QB are 'concerning'
Penn State head coach James Franklin voices his concerns over the death threats aimed at quarterback Sean Clifford and adds that sadly, "it's a part of our reality of our society right now."