Jack had only six carries all year prior to Friday's game and his lone touchdown this season had come on an interception return.
Given a chance to contribute in power offensive formations, Jack scored on runs of 8, 1, 1 and 2 yards. The four touchdowns were only one off the UCLA single-game record set nine years ago by Maurice Jones-Drew.
UCLA's other two touchdowns came on passes from Brett Hundley and the Bruins came up with a key fourth-quarter interception by Randall Goforth that protected a 10-point lead.
The Bruins are 8-2 for the season and improved to 5-2 in the Pac-12 Conference's South Division. Arizona State leads the division at 5-1 and hosts Oregon State on Saturday.
Arizona State will then travel to UCLA next week for a game that will determine the division champion. Washington fell to 6-4 and 3-4 in the North Division.
Hundley completed 13-of-22 passes for 159 yards without an interception. Jack carried 13 times for 59 yards. Two of his touchdowns came in the first quarter and UCLA built a 20-7 lead after one period.