They led 38-26 at intermission and got up by as much as 20 at the 14:37 mark of the second half before UTEP closed to within four down the stretch.
That's when Pledger--for the second straight contest--dropped in a clutch triple.
With 1:03 to go, he canned one from the right slot to make it 67-60, and the Sooners closed it out at the free throw line.
OU rattled off the first 15 points and held the Miners scoreless until after the first media timeout.
Forward Cedrick Lang finally got UTEP on the board with his only points of the game 5:17 into the contest.
While a pair of Sooners finished in double figures, three did so for the Miners.
Forward Chris Washburn scored 12, while guards Julian Washburn and Jacques Streeter each had 11.
OU narrowly outshot UTEP 41.7 percent to 41.3 percent.
It distributed 14 assists to 11 for the Miners.
The Sooners forced 17 turnovers, while they gave it up just 11 times.
They'll face 17th-ranked Gonzaga in the Semifinals round at 6 p.m. Friday.