Junior John Bohannon’s second career 3-pointer at the shot clock buzzer gave the Miners an 84-80 lead with 2:09 remaining in the third overtime, but Oregon was back within 86-84 before Tucker’s 3-pointer.
Julian Washburn led UTEP (4-5) with 23 points while Bohannon had 21.
Damyean Dotson scored 20 points and Carlos Emory had 18 for the Oregon (9-2).
At Oregon State 69, Howard 53: Eric Moreland and Roberto Nelson scored 14 points apiece, and Moreland added 10 rebounds and Nelson a career-high seven assists to help the Beavers beat the Bison.
Devon Collier added 12 points for Oregon State (8-2), which won its fourth straight game and improved to 6-0 at home.
Mike Phillips had 15 points, and Prince Okoroh 13 points for Howard (3-9).
Oregon State led by 10 at halftime and never let Howard get closer than eight in the second half.