Yonus Davis rushed for 143 yards and a touchdown as the Spartans (2-1) won at home for the 14th time in 16 games. Reed was 20-of-25 overall for 178 yards and an interception. David Richmond caught eight passes for 83 yards.
Freshman quarterback Ryan Lindley was held to 140 passing yards and was sacked four times as the Aztecs (0-3) lost their second straight to San Jose State.
Davis rushed for more than 100 yards for the first time in nearly two years. He was awarded a hardship exemption after missing all but a few minutes of two games last year. The sixth-year senior, who rushed for 1,007 yards as a junior in 2006, climbed into fourth place on the all-time rushing list with 1,984 yards.
The Spartans scored on three successive possessions within 11:08 of the first half to take a 21-0 lead.
Reed's 2-yard run with 2:45 left in the first quarter started the scoring. A key third down completion to Richmond set up the score.
Davis highlighted a seven-play, 89-yard drive with a 35-yard scoring jaunt early in the second quarter and Reed scored on a four-yard run five minutes later.
Aaron Moore picked off Reed's pass and returned it 28 yards for a touchdown with less than two minutes left in the first half.
Lane Yoshida's 36-yard field goal late in the third quarter made it 21-10 but Reed and backup quarterback Myles Eden each rushed for a score in the final period.
The Spartans outgained San Diego State by a 476-146 margin, the fewest total yards allowed by San Jose State under Dick Toomey. The Aztecs were held to six rushing yards.