Reed, who came over from California, was the third quarterback used by Spartans' coach Dick Tomey. He finished with 132 yards on 14-of-18 passing.
The Spartans got the ball back with just over a minute to play on their own 31 and no timeouts. Reed scrambled for nine yards and completed a 37-yard pass to Kevin Jurovich. Later on the drive, Stephen Wulff sacked Reed to force a fourth down.
Reed calmly sat in the pocket until Jurovich came clear in the end zone and fired it to his senior receiver, who caught 11 passes for 99 yards.
The Aggies' Daniel Alfaro threw his first college pass for a 54-yard touchdown. The junior quarterback, making his first career start because of an injury to sophomore Greg Denham, finished the game with 193 yards and a pair of interceptions. Bakari Grant caught eight passes for 108 yards and a touchdown.
Reed got the Spartans moving in the third quarter as he completed 11 of his first 12 passes, including three-yard touchdown pass to Terrance Williams to make it 10-6 with 2:07 left in the quarter.
Aggies' senior defensive lineman John Faletoese blocked the extra point try, the sixth of his career.
The Aggies nearly doubled San Jose State's offensive output in the first quarter, gaining 132 yards and scoring twice.
San Jose State, using two quarterbacks in the early going, lost a fumble and threw an interception.
After the Spartans opening drive ended in a missed field goal, UC Davis needed four plays and less than two minutes to take the early lead, with Alfaro finding Grant on a screen pass that went 54 yards for a 7-0 Aggies lead.
Jordan La Secla, the Spartans' second quarterback of the day, completed two passes and was then intercepted by Wulff and returned 23 yards to the San Jose State 18-yard line. That led to Sean Kelley's 20-yard field goal with under a minute to play in the first period.
Myles Eden started for the Spartans, throwing for 86 yards on 10-of-13 passing.