The Sooners were boosted by a breakout performance from guard Steven Pledger, who racked up a career-high 38 points, including 12 of the team's 15 points in the extra period.
That included seven triples in 13 attempts, part of 12-for-20 shooting from the field in the contest from the sharpshooter.
Following two straight outings where each Sooner starter scored in double figures, the only other player aside from Pledger to make it to that mark was guard Cameron Clark, who finished with 11.
Four Cyclones finished in double figures scoring, as forward Melvin Ejim led the way with a double-double of 19 points and 12 boards.
From the beginning, it appeared as though the Sooners might be able to manage a fairly routine road victory after suffering eight straight setbacks to open up the 2010-11 campaign.
But after OU led 34-19 late in the first half, that's when the Cyclones made their run.
They closed to within six points in the final minute of the first half before OU point guard Carl Blair buried a buzzer beater to put OU up 38-30 at intermission.
ISU carried that momentum into the second half, opening the final 20 minutes with a 7-0 spurt that left them down just one.
The Cyclones tied it up and then, following a stretch that allowed OU to build its lead back to seven, they stormed back to seize their first advantage of the game at 54-53 with just more than eight minutes remaining.
From that point, it was a seesaw battle that ISU appeared to take control of when they went up 67-61 in the final 3:35.
But the Sooners scored the final six points in regulation, the biggest of which was a three hit by Pledger with 35 ticks left.
In overtime, it also appeared as if the Cyclones might finally take control and run towards the finish line, as they led 72-69 with just more than three minutes left.
However, Pledger spawned a 10-0 Sooner run, and they never trailed again.
The win places the Sooners in a three-way tie for fifth in the Big 12 heading into a crucial contest against Baylor Tuesday night at Lloyd Noble Center.