Richards scored the first five points in overtime for the Wildcats (15-4), who blew a 10-point lead in second half and went the final six minutes of regulation without a field goal. His last two free throws came after he fouled when Terrence Shannon missed on awkward shot when defended by EJ Montgomery.
Texas Tech (12-7), which had won 54 consecutive non-conference home games since December 2013, had one last possession. But Davide Moretti was stripped by Ashton Hagans when starting a drive in the lane.
Immanuel Quickley had 21 points for the Wildcats, including a buzzer-beating 3-pointer from halfcourt that put them up 36-34 at halftime.
Kyler Edards had 18 points for the Red Raiders, while Moretti had 15 and Shannon 12.
Eight-time national champion Kentucky never trailed again after five points in the final five seconds of the first half. Tyrese Maxey made a contested one-handed floater before Chris Clarke's deep inbound pass went out of bounds with 1.6 seconds left. Montgomery then inbounded to Quickley, who took one dribble and let go of the shot from the half-court line.
But the Red Raiders, who made it to their first national championship game last year, tied the game with their opening shot of the second half. Moretti twice tied the game late in regulation with free throws, though the 92% shooter missed the first of two from the line with 18 seconds left.
Texas Tech missed another potential go-ahead free throw in overtime after Kevin McCullar was fouled when making a layup that made it 74-all with 31 seconds left in overtime.
BIG PICTURE
Kentucky: The Wildcats held on for an impressive road win in a raucous sold-out arena. While they blew the 10-point lead, they still improved to 257-7 when taking a lead of at least 10 points in a game in coach John Calipari's 11 seasons.
Texas Tech: The Red Raiders hadn't lost a non-conference game at home since LSU, another SEC team, won there Dec. 18, 2013. They had been 34-0 in four seasons under coach Chris Beard. Their 54-game non-conference home winning streak was second to Butler's 58 in a row.
UP NEXT
Kentucky is back home and back in SEC play against Vanderbilt on Wednesday night.
Texas Tech plays the second of three consecutive games against Top 25 teams. The Red Raiders host No. 14 West Virginia on Wednesday night before playing at No. 3 Kansas next Saturday.
