Colorado State (6-5, 3-3 Mountain West), which snapped a two-game losing streak and became bowl eligible, also got a 42-yard scoring run from Jimmy Green with 4:16 left.
Cornerback Ben Stratton got the Rams' lone touchdown in the first half, returning an interception 35 yards.
J.C. Mejia kicked 51- and 41-yard field goals to account for the only scores by the Aztecs (5-6, 2-4), who fell from bowl consideration.
SDSU lost quarterback Adam Hall early in the third quarter with an injury to his non-throwing hand.
The Rams were clinging to a 7-6 lead when Hill got loose behind the San Diego State secondary and hauled in Van Pelt's pass at the 30. Green added an insurance TD, bolting off the left side less than five minutes later.
In a first half dominated by defense, Colorado State went ahead 7-3 despite being outgained 207-128.
Each team mounted a long drive that ended on a missed field goal on its first possession.
On the first play of the second quarter, Stratton stepped in front of receiver Jermaine Moore and picked off Hall's pass, returning it for a score.
Moments later, Michael Franklin's 42-yard run set up Mejia's career-long 51-yard field goal.
Van Pelt then fumbled at the end of a 25-yard run, and linebacker Kirk Morrison recovered at the CSU 49. But SDSU couldn't convert as Mejia missed a 42-yard attempt.
Sacks killed scoring threats by both teams later in the half.
Mejia capped a 49-yard drive with a 41-yard field goal early in the third quarter, but the Aztecs lost Hall on that series.