Oklahoma State (19-5, 5-4 Big 12) rallied from 11 points down in regulation and trailed by seven with 1:30 left in the first overtime before having a chance to win in the final seconds of the period. Texas Tech's Martin Zeno blocked a layup attempt by Marcus Dove to force a second overtime.
The Cowboys scored the first six points to take an 89-83 lead, but Texas Tech (15-10, 4-6) rallied to tie it at 89 on a breakaway layup by Michael Prince with 33.9 seconds left.
Oklahoma State held for a final shot. David Monds missed a 15-footer, but Boggan rebounded and scored while being fouled with 4.1 seconds left. Boggan made the free throw.
Dove fouled Tech's Jarrius Jackson with 1.3 seconds left, and Jackson made both free throws. The Red Raiders fouled JamesOn Curry on the ensuing inbounds play, and he hit the first of two free throws. After he missed the second, Texas Tech's desperation heave fell well short.
Coming off consecutive road losses to Colorado and Oklahoma, the Cowboys extended their winning streak at Gallagher-Iba Arena to 17 games. Oklahoma State is 4-0 in overtime games this season, having also beaten Missouri State in one overtime, Pittsburgh in two overtimes and Texas in three overtimes.
Bob Knight's Texas Tech team has lost five straight since consecutive wins over ranked foes Kansas and Texas A&M. The Red Raiders have lost seven of eight against Oklahoma State and 18 of the last 23 meetings.
Jackson led the Red Raiders with 24 points, while Zeno added 21.
A 15-2 run, highlighted by two 3-pointers from Darryl Dora, gave Texas Tech a 50-39 lead with 15:13 left. Oklahoma State answered with eight straight points as Boggan hit a pair of 3-pointers, including one that hit off the back of the rim, caromed above the backboard and dropped through the basket.
The Cowboys regained the lead at 59-56 on a 3 by Curry with 7:26 left.
Texas Tech led 71-68 with 1:24 to go in regulation, but the Cowboys tied it on Byron Eaton's free throw with 31.2 seconds left. The Red Raiders had a chance to win in regulation, but Dora missed a well-guarded 18-footer at the buzzer.
In the first overtime, Texas Tech had what appeared to be a comfortable, seven-point lead with 90 seconds left. The Red Raiders still led 83-77 with 50.7 seconds to go, but the Cowboys closed with a flourish. Boggan's three-point play, after he rebounded a missed free throw by Curry, cut the margin to two, and Curry scored after Zeno turned the ball over while being double-teamed.
Jackson missed a layup for Tech before Zeno blocked Dove's last-second shot.
Curry and Terrel Harris scored 16 points each for Oklahoma State.