The stretch sandwiched around forward Romero Osby's two makes, which included 0-for-6 shooting from the field along with just 7-of-12 free throwing, allowed the Mavericks to cut what was once a 17-point lead to two at the time.
UT-Arlington would ultimately tie it up but could never again regain the lead after getting up by as much as nine in the first half.
When a bucket by Maverick forward Jordan Reves knotted it up at 60 with just 2:35 to play, that's when the Sooners got a veteran shot by senior guard Steven Pledger.
Pledger canned a triple to put OU up three, and it rode that to the finish as he downed the eventual dagger at the line to make it a four-point lead with just a few ticks left.
Despite going silent in the second half, guard Buddy Hield led the Sooners with his game-high 17 points, all of which came in the opening 20 minutes.
Osby poured in 10.
A pair of Mavericks also managed double figures, as forwards Kevin Butler and Karol Gruszecki scored 16 and 15, respectively.
UT-Arlington actually outshot OU, hitting an even 40 percent to the visitors' 35.2 percent and holding a 32-24 advantage in the paint.
But the Sooners got to the stripe 11 more times than the Mavericks and, although they didn't shoot it well there while going 20-of-32, converted just one less free throw than UT-Arlington hoisted.
The Mavericks finished 12-for-21.
A cold start from the guys north of the Red River allowed UT-Arlington to leap out to a 12-3 lead at the first media timeout.
It also had that margin a couple minutes later at 16-7 and held an eight-point lead when it was 19-11 just more than halfway through the first half, but then the Sooners got to work.
They used an 11-0 run over the next 2:49 to reclaim the lead for good.
The Sooners were up 38-28 at intermission and extended on that after the break before the drought and furious rally.
OU (2-0) will get back to action when it heads to the Old Spice Classic a week from tomorrow and opens up with a 6 p.m. CT tipoff against the UTEP Miners in Orlando, Fla.