For California (7-6), ranked No. 2 in October before losing six of seven games, the win meant a sixth winning season in a row.
Jackson, Jordan and leading tackler Thomas DeCoud were held out of the starting lineup and didn't play the first quarter because of unspecified violations of team rules.
Helped by a botched kickoff, Air Force (9-4) led 21-0 after scoring twice in a 2-minute span early in the second quarter.
But Jackson made an acrobatic 40-yard touchdown catch to cap his first drive, and Jordan had an 18-yard scoring grab in the third quarter. Jordan finished with six catches for 148 yards, and Jackson caught five passes for 81 yards.
Justin Forsett ran for 140 yards and two touchdowns on 23 carries. His 1-yard score late in the third quarter put the Bears ahead for good at 28-27.
Freshman quarterback Kevin Riley, who took over for Nate Longshore in the second quarter, was 16-for-19 passing for 269 yards and three touchowns, adding a rushing score. Longshore had a nagging sprained right ankle, and coach Jeff Tedford wanted to get Riley some action.
Air Force lost four-year starting quarterback Shaun Carney because of a right knee injury when his leg buckled awkwardly while being tackled.
The Falcons, who were denied their first double-digit win season since 1998, were playing in their first bowl since 2002.