Tolbert added 12 rebounds before fouling out with 1:36 left in overtime. It was Tolbert's fifth career double-double and the third double-double of the season for the junior.
Toddrick Gotcher added a career-high 17 points and five assists, Jaye Crockett scored 15 points and Dusty Hannahs added 14 for Texas Tech (8-7, 0-2). Crockett is now two points shy of 1,000 career points in 108 career games.
The Red Raiders faced an 11-point deficit early in the second half, but Hannahs and Crockett came alive to regain the Red Raiders first lead since the opening minutes. Tech led 77-74 in the final minute of regulation, but Henderson hit a 3-pointer with 16 seconds left to force overtime.
Crockett missed a 3-pointer at the buzzer that would have forced a second overtime.
Eron Harris added 18 points and Terry Henderson scored 16 for the Mountaineers (10-5, 2-0 Big 12).
It was the third straight meeting between the two teams that has been decided by three points or less. West Virginia won in Morgantown last year, 66-64 and the Red Raiders defeated the Mountaineers 71-69 in the Phillips 66 Big 12 Championship first round last March.
In all, the game featured seven lead changes and four ties.