Twice in the contest the Sooners threatened to open up a double-digit lead, but both times the Aggies stormed back into it.
The latest came when OU held a 53-46 advantage after guard Steven Pledger drilled a 3-pointer with 10:46 to go.
A&M bounced back to tie it at 60 near the five minute mark.
From that point on, it was a true seesaw battle, one in which the Sooners appeared to be putting the finishing touches on with a minute remaining.
That's when forward Andrew Fitzgerald drained a beautiful jumper from the left corner after getting hammered.
He completed the traditional 3-point play to give OU a 65-62 lead with exactly a minute left.
But Aggie guard Elston Turner hit a game-tying triple moments later, and the Sooners' attempt to win it at the buzzer clanked off the iron.
The Aggies then dominated the overtime period on their way to victory.
It couldn't have been a more evenly matched game from the beginning.
Neither team ever led by double digits and both halves ended in ties.
The two were locked at 34 after the first 20 minutes and each scored 31 in the second half.
Along with Osby, Fitzgerald and Pledger also scored in double figures, with 17 and 16, respectively.
Turner led all scorers with his 23, while forward David Loubeau added 16, and guard Dash Harris had 14.
OU (12-6 overall) drops into a four-way tie for sixth place in the conference with its 2-4 mark.
The Sooners get a couple of days off before returning to Lloyd Noble Center for a 7 p.m. date with the 17-2 Baylor Bears.