A "White-Out" crowd of 7,801 watched as the Rainbow Warriors improved to 12-5 overall and 4-5 in the Western Athletic Conference.
Sottos scored 23 of his career-high 25 points in the second half, while Sensley scored 14 of his 21 points in the period. At one point in the half, the duo combined to score the team's first 26 points and helped erase an early 12-point second half deficit.
UH shot 53.1 percent in the second half and sank eight of 13 shots from beyond the 3-point arc.
The teams traded baskets and leads to start the game until TU surged ahead 21-12 lead. The Golden Hurricane jumped out to a 29-18 advantage before the 'Bows closed out the half with a 12-7 run to trail 36-30.
The 'Bows shot just 37.5 percent in the period and converted only one of seven 3-point attempts.
Tulsa (4-14, 1-8) scored the first six points of the second half to take its largest lead at 42-30. UH answered back with a 13-0 run behind seven points by Sensley and six by Sottos to take a one-point lead.
Moments later, Sottos' third trey and lay-up put the `Bows ahead 48-44. After the Hurricane tied it at 51, Sensley's one-handed alley-oop dunk and Sottos' fourth trey gave UH a five-point cushion with 8:39 remaining.
After TU closed to 57-56, a Bobby Nash trey and Vaidotas Peciukas layup put UH on top 62-56. Sottos' fifth trey extended the Hawai'i lead to 67-60 with 3:54 left. Tulsa would get no closer than four points the rest of the way until a Tulsa trey to end the game created the final margin.
The Golden Hurricane were led by Anthony Price's 23 points and eight rebounds.
The 'Bows embark on their longest road trip of the season, beginning at San Jose State, Feb. 5. UH will also face Louisiana Tech, Feb. 10, and SMU, Feb. 12.