Wilcox has now scored at least 15 points in 15 straight games and 58 times in his career. Andrew Andrews added 19 for Washington (8-5).
Hartford led much of the game, but Wilcox put the Huskies ahead 53-52 with a pair of free throws with 7:24 left. Those points moved him into eighth spot on the school's all-time scoring list, now with 1,559 points. He passed James Edwards (1974-77).
The Huskies, fourth in the nation coming in with 76.5 free-throw percentage, made 13 of 15 over the final 7:30 for the winning edge. For the game, the Huskies connected on 26 of 30 attempts (86.7 percent). Hartford was 10 of 13.
Mark Nwakamma led the Hawks (5-9) with 21 points. Nate Sikma, who grew up in Bellevue and is the son of former Sonics center Jack Sikma, had 16 points.
With 5:01 left, Corban Wroe fouled Wilcox then was given with a technical foul for taunting.
Wilcox, an 89.7 percent free-throw shooter, then made three of four attempts for a 61-57 lead, matching the Huskies largest lead to that point.
But the Hawks bounced back and took a 65-63 lead with 2:28 left on Evan Cooper's fast-break lay-in.
Wilcox and Nigel Williams-Goss followed with back-to-back 18-footers to give the Huskies a 67-65 lead with 1:12 left.
With the Huskies leading 69-67 coming out of a timeout with 19.1 seconds left, Wilcox was fouled on an attempted lay-in and made both free throws.
After Cooper missed on the other end, Desmond Simmons was fouled and he made both free throws to end it.
Hartford, on the strength of three straight 3-pointers, built an early 11-6 lead. Washington needed another six minutes to finally pass the Hawks 19-18 on a fast-break basket by Jahmel Taylor with 10:15 left.
Behind Nwakamma's 11 first-half points, the Hawks went ahead 26-21 with four minutes left.
It took a Williams-Goss 3-pointer with a minute left to give the Huskies a 31-29 lead at intermission. It was the second fewest points at halftime for the Huskies this season.
Andrews, making five of six free throws in the final three minutes, led the Huskies with 13 points in the first half.