Bruins Coach Jim Mora met him near midfield and barely shook Snyder's hand. It was part of a tense finish that had Mora firing off a provocative comment on his Twitter site later.
"I will defend the safety of my players forever," Mora posted.
Quarterback Brett Hundley, receiver Jordan Payton, defensive back Ishmael Adams and other players posted: "Thank you Coach Mora for protecting the team."
The Bruins were in the "victory formation" with Hundley taking a knee for three plays. On the last one, following a Kansas State timeout, a Wildcats' player hurled himself over the line and at Hundley. He was met by UCLA's Eddie Vanderdoes before he could hit Hundley.
The game, though was edgy before that.
"They were getting frustrated," UCLA linebacker Deon Hollins said. "It was getting chippy."
Hollins said he tried to shake Wildcats lineman Cody Whitehair's hand after the game, "but he didn't want to."
Mora denied any deeper meaning to the quick handshake with Snyder.
"I'm not sure what you're talking about, I'm sorry," Mora said. "It was just a normal handshake to congratulate him."
Mora said he even shook Snyder's hand a second time. "I ran into him as I was working [my way] back to the podium," Mora said.
UCLA opponents have become used to linebacker Myles Jack being a problem. They may have to worry more about Hollins as well.
Hollins finished with three of UCLA's season-high seven sacks Friday.
"I think Deon really put it all together this year," Jack said. "He's my roommate when we travel. I know how hungry he was to help this team. I think he was frustrated last year and was eager to get back on the field."
Jack's 41-yard interception return in the second quarter set up a 32-yard touchdown run by Paul Perkins.
"We're going to run things," Hollins said. "Myles and I talk about that all the time."
The Wildcats were unable to budge the Bruins, finishing with 31 yards rushing. But Jake Waters' passing nearly brought the Wildcats back. He completed 31 of 48 passes for 338 yards and two touchdowns.
Hundley finished his three-year UCLA career with 9,966 yards passing and 1,747 rushing, both second in school history. He accounted for 106 touchdowns, throwing for 75, running for 30 and catching one.
UCLA receiver Kenneth Walker III did not come to San Antonio with the team because of an academic issue.
Follow Chris Foster on Twitter @cfosterlatimes