TULSA, Okla. -- Stanford's Taylor Davidson fought off a match point for 3-6, 7-5, 7-5 victory over Oklahoma State's Vladica Babic that gave the Cardinal a 4-3 win and their 18th NCAA women's tennis championship on Tuesday.

Babic won the first set 6-3 and had match point at 5-4 in the second, but Davidson rallied for the title-clinching win, the team's first since 2013.

"They always feel really good," said Stanford coach Lele Forood, who won her eighth title. "Very satisfying. They gave us almost more than we could handle, obviously, today. It was an incredible match, it was very back and forth, there were up and downs, it was amazing."

After Viktoriya Lushkova beat Stanford's Caroline Doyle 4-6, 6-4, 6-1 in No. 3 singles, No. 12 Oklahoma State (29-5) led the team competition 3-1. But the No. 15 Cardinal (20-5) came back and won the next two matches.

Caroline Lampl and Melissa Lord won their Nos. 5 and 6 singles matches after each lost the first set for Oklahoma State, setting up the Davidson-Babic No. 2 singles match as the one to decide the title.

"I was down 4-1, 5-2, I think there was actually a match point against me at one point," Davidson said. "Honestly, I wasn't thinking, `I need to come back and win this match,' I was thinking, `Stay on the court, maybe (No. 1 singles player Carol Zhao) can split sets,' because I know how nice it is to not have as much pressure on your shoulders and play under a more relaxed environment. `Just stay on the court."

Davidson did, and with the momentum on her side, went up 5-2 in the third set, but just as it became clear that their match was going to decide the championship, Babic fought back to tie it 5-5 before Davidson won the final two points.

"I kind of had a feeling it was down to me," Davidson said. "And I had a pretty big lead, I was up 5-2, she was making errors, and then I started cramping a little bit, things didn't feel as good. I knew that if I could just stay in the match, make her hit a lot of balls, that I was tougher than her, but at that point, there's just so much pressure on both players, you don't know what's going to happen."

Oklahoma State, which had never previously advanced beyond the Sweet 16, was attempting to win its first national championship in any women's sport.

The Cowgirls had a huge contingent of fans in attendance that cheered them loudly throughout the match.

"What a day," coach Chris Young said. "For Oklahoma State to be in this position, in Tulsa, to have so many (fans) come support us, just means so much to us. We're not supposed to be here. But we fought as hard as we possibly could, these girls gave me everything they had, and I think there's two champions out here today."

It was the first NCAA women's championship match that did not feature any top-10 seeds.