Mulkey said that Baylor wasn't used to playing close games during its streak.
"We didn't respond very well, we got back in the game but we didn't execute some things and we didn't do some things defensively," Mulkey said.
While the Lady Bears returned mostly intact this year, Stanford lost All-American center Nnemkadi Ogwumike to graduation after last season.
The untelevised afternoon game in Honolulu was played in a mostly empty Stan Sheriff Center, an arena modeled after Baylor's home floor in Waco, Texas.
Without Sims, the Lady Bears trailed by 14 points before rallying to 31-29 at the break. Stanford focused on Griner on defense and took advantages of missteps by Baylor on the other end to get second chances and open looks.
Griner was dominant in the second half, scoring 10 of Baylor's first 12 points and just under half its points for the final half. The Lady Bears gave up on shooting 3-pointers, allowing Griner to carry them. The attempted only three after ending the first half 1 for 11.
Baylor took a 55-54 lead with 7:11 left in the game on a layup from Williams. It was the Lady Bears first lead since early in the first half. They extended it to four points before Stanford rallied behind Kokenis, who made two free throws and a jumper to tie it at 60.
The game was back and forth until the final minute when Tinkle and Chiney Ogwumike gave Stanford the lead for good.
Ogwumike was one of four Stanford players to score in double digits. Taylor Greenfield had 16 points, Kokenis had 15 and Tinkle had 11.
Mulkey said the team will use the loss as motivation.
"You don't ever want to lose. You're in Hawaii, you're not under the normal circumstances of a regular practice schedule. You're enjoying the beach and not having as much time to prepare," Mulkey said. "We played Kentucky and had a quick turnaround to come here. It's a great schedule for us to prepare for another national championship."
Oskar Garcia can be reached on Twitter at http://twitter.com/oskargarcia .