OU improved to 31-13 overall and 10-9 in Big 12 play with the win.
Head coach Sunny Golloway got a good outing from the two-headed monster, made up of senior pitcher Bobby Shore and freshman pitcher Dillon Overton, and a solid although not overpowering day from his lineup.
Shore, who has been battling tendinitis in the past month, left the game in the fourth with a forearm injury in his throwing arm.
But the senior was having his best start in conference play before the injury forced him out.
One of the reasons why he looked so comfortable on the mound was because he was working with an early two-run lead.
Junior catcher Tyler Ogle doubled in the game's first run in the third and scored a batter later after Buechele reached on an error by the shortstop. Buechele's grounder went off Texas shortstop Brandon Loy's glove and trickled into left field with two outs, so Ogle was able to score easily on the play.
Texas senior first baseman Tant Shepherd, who was the only Longhorn who had a multi-hit game in the finale, cut the Sooners' lead down to one with a solo homer in the fourth.
The homer would be the last full at-bat Shore would throw as he was pulled during the next batter.
He lasted 3 1/3 innings, allowed one run on two hits – both to Shepherd – and struck out three.
Overton took over and silenced the Longhorns while his offense built up a three-run lead.
Junior center fielder Erik Ross plated two runs in the fourth with a triple to deep center to put the Sooners up 4-1. It was his second extra-base hit and first triple of the season.
The only time Texas truly threatened OU's lead while Overton was in the game was in the sixth inning.
Overton loaded the bases with two singles and a two-out walk but got out of the jam by striking out sophomore left fielder Jonathan Walsh on a chest-high full-count fastball.
Sophomore left fielder Max White tacked on another insurance run in the seventh with a solo shot well over the wall in left. The homer was his third of the season.
Overton threw two more solid innings after the bases-loaded jam in the sixth.
He allowed two hits and struck out three batters in 4 2/3 shutout innings to improve to 7-3.
Senior closer Ryan Duke struggled a bit in the ninth by giving up a run and allowing the tying run to come to the plate but closed out the game to secure OU's first victory against Texas since 2008.
The Sooners head out to Little Rock, Ark., to take on the Arkansas-Little Rock Trojans at 6 p.m. Wednesday. OU took two of three games against the Trojans in a weekend set in Norman in March.