Pitcher Jonathan Gray picked up his seventh win after settling down from the second inning on.
Gray gave up a two-run homer in the top of the first, but was very solid after that.
He fanned nine and kept Samford off the scoreboard again despite surrendering eight hits and two walks.
"It was pretty frustrating, but I also knew there was a pretty good chance some balls we're gonna leave the yard with the way the wind was blowing," Gray said. "I made an adjustment after that. I started getting ahead of hitters. I kept myself out of those situations."
Meanwhile, the offense did its part to put him out front, pounding out nine hits for six runs in the contest.
OU took the lead for good in the fourth on third baseman Garrett Carey's two-run single that made it 3-2 at the time.
"The key was getting Jon Gray the lead," said OU head coach Sunny Golloway. "From the fourth inning on, he looked really good. When we get the lead, you can just see him relax and he becomes a better pitcher."
The Sooners added another in the fifth when center fielder Max White doubled, advanced to third and scored on a wild pitch.
All but two starters in OU's lineup recorded a hit, and Mayfield and White each had two.
Closer Steven Okert came out of the bullpen to earn his fourth save of the season, dealing two scoreless innings, while striking out a batter and giving up two hits.
OU trailed by two until the third inning when Carey scored on a double play ball. That preceded his huge bases-loaded hit to put OU on top the next inning.
"Baseball will find its way back to you," Carey said. "Coach G says it all the time and it's true. I had two situations just like those last night and I didn't capitalize. Luckily, the game found me again and I was able to come through."
The two will battle for the series victory at 2 p.m. Saturday.