This was the Red Raiders' (14-17, 6-12 Big 12) first win over the Longhorns (22-9, 11-7) since 2008 in Lubbock.
Jordan Tolbert added 11 points and grabbed five rebounds for the Red Raiders, and Robert Turner added nine points, five rebounds and three assists.
The Red Raiders were down 44-37 with 9:23 left, but Crockett, a senior, wasn't ready to watch the last home game of his career slip away.
Tech pieced together an 18-4 run as Tolbert followed a Crockett 3-pointer with one of his own with 1:07 left to make it 55-48 and put the game out of reach.
Seniors Jamal Williams Jr. and Kader Tapsoba joined usual starters, seniors Crockett and Dejan Kravic and junior Turner, in the starting lineup for senior day.
The two teams exchanged buckets in the early minutes of the game and paced through a slow defensive battle. Tied 8-8 with 13:19 in the half, Texas worked to try to pull away, but couldn't widen the gap by more than six and took a 23-21 lead into the half.
It was the same back-and-forth battle in the opening minutes of the second half until the Red Raiders finally broke through for their first lead in almost 17 minutes with a Tolbert dunk to put them up 29-27 with 16:35 to go.
The lead didn't last long as Walker, Ridley and Connor Lammert kept Texas within reach before a 7-0 run, capped off with a Walker 3-pointer with 12:19 left, put the Longhorns back in front 38-33.
The teams exchanged buckets for a few minutes until a Marcus Holland layup bumped the lead to seven, the Longhorns' largest of the night, 44-37, with 9:23 to go.
Tech's Kravic displayed athleticism for a 7-footer when he saved a would-be out-of-bounds ball that found its way into Randy Onwuasor's hands. Onwuasor missed an off-balance layup but Kravic answered with one and drew a foul to set up a possible 3-point play.
The shot from the line didn't fall but the fans at the United Spirit Arena began to sense that a comeback might be brewing.
Toddrick Gotcher made a pair of free throws to cap off an 8-1 run and tie it 45-45 with 6 minutes to go.
The crowd erupted when Crockett slammed down an alley-oop from Gotcher with 4:45 to go to put Tech up 49-46.
Jonathan Holmes then made a pair of free throws to cut it back to one until the home crowd and the home team took over when Crockett drained a 3-pointer with just a few seconds left on the shot clock to boost Texas Tech ahead 52-48 with 1:56 left in the game.
Tolbert followed suit with a 3-point shot that swirled through the net and secured the win with 1:07 to go as the junior became the 37th Red Raider in history to score 1,000 career points.
The two late 3-pointers were the only ones of the game for the Red Raiders, who were 2 of 12 from long range.
Texas was forced to foul but the Red Raiders' ace free-throw shooter, Dusty Hannahs, made all four in the final minute to send the seniors out in style.
Despite making obvious progress in his first year as Texas Tech coach, Tubby Smith, with a 14-17 record, is facing his first losing season in 23 years of being a head coach.