The Bulldogs entered the game averaging 87.5 points and had not scored fewer than 68 this season.
"We just missed a lot of wide open shots," Gonzaga coach Mark Few said. "That and not getting to the free throw line were huge for us."
Kansas State was 19 of 25 from the foul line while the Bulldogs were 7 of 15.
Gonzaga played the second half without second-leading scorer Sam Dower, who took a hard fall late in the first half and did not return.
"He was in a lot of pain in his lower back," Few said. "(The doctors) were so concerned, they took him for an X-ray."
Southwell kept his team's momentum going right after halftime, scoring five straight to give the Wildcats a 33-24 lead with 18:46 to play.
Then Foster, a freshman among the top 10 scorers in the Big 12, had his stretch, going on a personal 7-3 run with a 3-pointer, a layup and monster slam over Stockton.
The Wildcats led 40-32 and the crowd was buzzing.
"Marcus is so athletic," said Southwell, who made the pass to Foster on the play for one of his six assists. "As soon as he got it and could get up, I knew it was over for Stockton."
But the Bulldogs answered as Gary Bell's 3-pointer capped a 7-0 run that pulled the Bulldogs within 40-39 with 14:48 to play.
After that, the teams exchanged the lead eight times in six minutes.
"The tempo had been at their tempo, but we were able to finally get it up and down a little and get back in the game," Few said. "We were in position. But then they made all the plays from that moment forward."
Gipson was the key. Twice then 6-foot-7 Gipson posted up the tiring Karnowski, a 7-footer forced into extended minutes by Dower's injury, for baskets.
The second one gave Kansas State a 60-54 lead with 3:39 remaining. Karnowski entered the game averaging 23 minutes but played 30 Saturday, 17 of them in the second half.
"He was definitely tired," Few said.
Gipson's putback with 1:59 to play pushed the lead to eight, and the Wildcats could milk out a victory from there.
"I just wanted to be active -- ball screen, roll and get posted up down low," Gipson said. "I knew I could get offensive rebounds or easy hook shots."
Gonzaga, among the top 20 nationally in scoring, had real difficulties finding its offense in the first half.
The Bulldogs had just 19 points in the game's first 17 minutes and trailed by five.
But Kyle Dranginis followed a driving layup with a 3-pointer, making the score 24-24 with 1:49 remaining in the half.
Kansas State scored the half's final five points on a 3 by Nigel Johnson and a layup by Nino Williams for a 29-24 lead. Gonzaga had not scored fewer than 31 points in a first half this season.