Northwest Division-leading Utah led by as many as 24 points before Washington got within six with just over 2 minutes left. Hayward hit a pair of jumpers to seal the win.
George Hill added 21 points for Utah.
Washington, the Southeast Division leader, has lost two in a row for the first time since early January. John Wall led the Wizards with 23 points and 11 assists. Bradley Beal, who was scoreless in the first half, added 22 points.
Utah converted 23 of 32 free throws, while Washington made 10 of 13. The Jazz outrebounded the Wizards 52-27.
Utah led 49-39 at halftime and opened a 62-43 lead with 6:48 left in the third quarter on Derrick Favors‘ dunk off a feed from Gobert, necessitating Wizards coach Scott Brooks’ second timeout of the quarter.
Consecutive 3-pointers by Hill soon increased the lead to 24.
Bojan Bogdanovic‘s 33-footer capped a 14-3 Wizards run to end the quarter and Utah’s lead was 73-60 to start the fourth.
Washington trailed by 16 when Wall hit a 3 and Beal followed with five quick points to make it 93-85 with 3:11 remaining. Bogdanovic’s two free throws cut the deficit to six at the 2:01 mark, but Hayward sandwiched a 3-pointer and a long 2 around a Washington turnover to stall the rally.
The Jazz shot 50 percent from the field and hit 13 of 18 free throws in the first half to build a 10-point lead.
The margin could have been bigger but Utah turned the ball over 14 times, leading to 15 Washington points. The Wizards shot 36.7 percent (18 of 49) and made their only free throw attempt.
After scoring 40 points in his previous game, Beal went to the bench with 5:08 left in the first half with three fouls and no points.
Jazz: Gobert was fined $25,000 for making physical contact with an official in the third quarter of Utah’s 109-95 victory over the Milwaukee Bucks on Friday. . Rodney Hood, who had three points Friday night in his return after missing seven games with a bone contusion in his knee, had nine points in the first quarter. . It was Utah’s first win in Washington since Nov. 17, 2012.
Wizards: The 39 points were the team’s lowest first-half total of the season. . Washington had reached 100 points in 23 straight games. . It was Wall’s 37th double-double of the season. . Bogdanovic, in his second game with Washington, scored 15 points. . Washington last lost two in a row on Jan. 2-3 in back-to-back road games at Houston and Dallas.
Jazz: Travel to Oklahoma City on Tuesday for the finale of a three-game road trip.
Wizards: Host the Warriors on Tuesday night.