Peters distanced 7 2/3 innings while striking out five and limiting OU to a season-low two hits in a 1-0 Saturday shutout that evened the series at a game apiece.
Texas closer Corey Knebel relieved him with 1 2/3 perfect innings to pick up his Big 12-leading seventh save of the year.
With that, he pulled Texas out of a two-on, two-out jam in the eighth.
Sooner first baseman Kolbey Carpenter got that started with a leadoff double smashed off the left field wall, before he was picked off.
"With the wind blowing out, knowing that we have some power, they were going to stay away [from pitching over the plate]," said OU head coach Sunny Golloway. "Carpenter was able to turn on a ball that almost got out. Again, that was just their philosophy, to stay away, and they weren't going to get hit very many times."
The Longhorns certainly didn't do much damage off Overton either, though.
In fact, their only run came in the bottom of the fifth when designated hitter Ben Johnson brought home left fielder Mark Gottsacker on an RBI single to center.
Aside from that, Overton was phenomenal.
"It was one of the best outings I've had all season," Overton said. "I felt good. Baseball is a tough sport and sometimes that happens. They just got one timely hit and that's what put them over the top. Their pitcher did a great job also and I tip my cap to him."
For the second straight game after posting an OU record 30-game hitting streak, designated hitter Matt Oberste was held hitless.
Only Carpenter and third baseman Garrett Carey recorded hits for OU.
The two will complete the series with a rubber match Sunday at 2 p.m.