Balance, and 56 percent shooting in the first half, made the difference for the Huskies (6-4). Nigel Williams-Goss and Perris Blackwell added 12 points and Mike Anderson had 10.
Wilcox moved past the 1,500 point plateau and into 11th on the UW scoring list despite his lowest-scoring game of the season.
"We did a good job on defense early then kind of relaxed," Wilcox said. "We got in foul trouble and they took advantage. We came out a little flat in the second half and they stayed close."
Freshman Jonathan Stark matched his career high with 25 points, 17 in the first half when he kept Tulane (5-6) in the game. Louis Dabney added 16. Jay Hook, who had 31 points in the last game with a school record eight 3-pointers, was held to eight, just two in the second half and that was the only 3 for the Green Wave in 14 attempts.
"Credit Washington," Tulane coach Ed Conroy said. "Defensively their athleticism on the perimeter and their quickness closed down gaps and made it hard for us to beat them from three."
Tulane scored the first basket but then proceeded to shoot 32 percent in the first half, including a 1-9 performance from 3-point range and 13 of 21 from the foul line. Despite battling foul problems and turnovers the Huskies grabbed a 41-32 when Wilcox dropped a half-court buzzer beater. That made UW 6 of 12 from behind the arc at the break.
"We practice it every day at the end of practice, work on trick shots," Wilcox said. "I had an opportunity to take advantage tonight and it worked out."
The Green Wave shot better in the second half and got within three on Dabney's three-point play at 12:40. But UW always had someone come up with a key basket to hold off the Green Wave.
Washington ended up with a season-high 18 turnovers but Tulane's poor shooting made it difficult to take advantage and then the Green Wave had foul issues in the second half. The Huskies didn't make a field goal for the last 7:51 but they knocked down their free throws, making 15 of 20 in the second half to finish 22 of 28. Eleven of those makes came down the stretch.
Still, the Huskies didn't pull away because they shot just 38 percent in the second half, making 1 of 9 3's.
"In the second half we couldn't put the ball in the basket," UW coach Lorenzo Romar said. "We had three people in foul trouble in the first half and when we subbed (the offense struggled). We had to mix and match and kind of survive it. ... We made it a lot harder than it needed to be."
Stark, who leads the nation in minutes played at 38 1/2 per game, played 35. He missed two crucial minutes with an apparent cramp at 5:46, just after he missed a layup. As he left, Andre Andrews hit two free throws for a 66-57 Washington lead.
The Huskies had an 18-7 advantage in scoring off the bench.