The Tigers, playing their season opener under second-year coach Damon Stoudamire, cut a 25-point deficit to five points with almost two minutes remaining in regulation.
Pacific guard Lafayette Dorsey, who made a 3-pointer to cut the lead to 85-80 with 2:17 remaining, missed the chance to minimize the lead more when he did not convert from beyond the arc with 1:28 left.
The Tigers missed their last three shots in the final two minutes of the game.
Oscar Da Silva and Humphrey each made one of two shots at the free-throw line on subsequent possessions to give Stanford an 87-80 lead.
Two free throws by Robert Cartwright with 29 seconds left sealed the win for the Cardinal, which is 2-0 in coach Jerod Haase's second season.
Reid Travis contributed 23 points and six rebounds and Dorian Pickens had 11 points for Stanford.
Miles Reynolds led Pacific with 20 points.
Four of the Tigers fouled out, including Anthony Townes (10 rebounds) and Namdi Okonkwo (10 points).
The Tigers' 1-3-1 zone defense implemented by Stoudamire in the second half seemed to unsettle the Cardinal, which shot only 16.7 percent from 3-point range and committed seven turnovers after halftime.
Stanford, which never trailed after 15:55 remained in the first half, built a 53-31 lead at halftime behind 16 points and 10 rebounds by Humphrey.
A 20-4 run by Stanford in the middle of the first half broke the game open to a 29-12 lead.