The win was the fourth in row for the Aztecs (7-2, 4-1 Mountain West), who play at fourth-ranked TCU next week.
Pete Thomas was 22 of 40 passing for 266 yards for the Rams (3-7, 2-4).
Hillman became the third San Diego State freshman to rush for over 1,000 yards in a season, joining Marshall Faulk (1991) and Lionel Hamilton (1994). He scored his 12th TD of the year from 26 yards to give the Aztecs a 17-13 lead in the third quarter.
Brandon Sullivan scored his second touchdown when he caught a 16-yard pass from quarterback Ryan Lindley with 8:05 left in the game, putting San Diego State up 24-13.
The Rams pulled to within 24-19 when Thomas connected with Zac Pauga on a 28-yard screen pass for a TD with 2:43 to play.
Late in the third quarter, Lindley was stripped of the ball by Colorado State linebacker Mychal Sisson, who raced 88 yards for a touchdown to give the Rams a 13-10 lead.