Wilcox scored 27 points and made a pair of crucial 3-pointers as the Huskies held off Stanford 65-60.
"We knew we had to keep getting him touches," Romar said. "He's a pretty prolific shooter. We kept trying to find ways to spring him loose."
Aziz N'Diaye added 14 points as the Huskies (11-5, 3-0 Pac-12) opened conference play with three straight wins on the road for the first time since 1912. Desmond Simmons added 13 rebounds.
"I've never been part of anything like this," Romar said. "We've had plenty of successes over the years, but never gone on the road and won our first three."
Dwight Powell scored 19 points to lead the Cardinal (10-7, 1-3), who have lost three of four.
"We have been competitive in every single game," Stanford coach Johnny Dawkins said. "It's a matter of us getting over the hump. We're a good team and we have to continue to work like one."
The Cardinal shot 26.7 percent from the field (8 of 30) in the second half after finding the basket 51.7 percent of the time (15 of 29) in the first half.
"It's very disappointing," Powell said. "We have high expectations of ourselves. We'll bounce back."
The lead changed hands 15 times and was tied on nine occasions before the Huskies gained a foothold early in the second half.
Wilcox, who finished a point shy of matching his career high, hit a 3-pointer to give Washington a 52-44 advantage, the largest lead of the night, with 9:56 remaining.
"They were guarding him pretty good, trailing him everywhere, being physical with him," Romar said. "He did an amazing job against that defense."
Wilcox added a career-high nine rebounds and scored 13 of Washington's final 15 points.
"Coach told us to be aggressive and look for me off screens," Wilcox said. "I was feeling it. He told me to take my shots."
The Huskies went scoreless for four minutes. The Cardinal had several chances to tie it, but managed only to cut the lead to 52-50 before another Wilcox 3-pointer broke the drought.
Chasson Randle hit a jumper to tie it again at 58 with 3:26 left, but Washington hit its next four free throws to regain the advantage.
Randle, who did not start due to an infraction of team rules, was 6 of 7 from the floor during the first half as Stanford took a 36-35 lead into intermission.
Halftime activities included the honoring of Stanford's Rose Bowl champions. Offensive coordinator Pep Hamilton made a half-court shot, the only successful attempt among players and coaches.