The Wildcats avoided what almost became their second upset loss in three contests to move within one game of Oregon for the lead in the Pacific-12 Conference. Arizona suffered a home loss to UCLA last week.
Washington led by as many as 11 in the first half, but Arizona inched in front midway through the second period and fought off the Huskies in the late going.
The Huskies' Aziz N'Diaye missed two foul shots with 1:36 to play that would have given Washington the lead and Hill then put Arizona in front by three by hitting a jumper with 1:21 left.
Scott Suggs hit a layup for Washington to make it a one-point game with 1:12 to go, but the Huskies did not score again. They missed two layups and a 3-point try in addition to suffering a turnover while Johnson was converting 3-of-4 free throws to secure the win.
Johnson scored 15 points to lead the Wildcats (18-2, 6-2 Pac-12). Arizona won despite making only 35 percent of its shots and converting a mere 3-of-18 from 3-point range.
Washington (12-9, 4-4) was paced by Suggs and C.J. Wilcox with 11 each.