Thirteen of Dickerson's points came in the final five minutes as Washington fought to take and hold the lead.
Nowell sealed the game for the Huskies (8-3) with an off-balance jumper with 30 seconds left as the shot clock was winding down, giving Washington a four-point lead.
Washington big man Sam Timmons had nine points and a season-high 11 rebounds before fouling out with five minutes to play.
Washington trailed 34-28 at halftime, going more than seven minutes without a field goal -- on 0-for-11 shooting -- to end the first half.
Washington turned it around quickly in the second half, going on an early 11-0 run featuring several dunks.
Loyola Marymount: This was the second time this season the Lions lost a close game against a Pac-12 opponent. Loyola Marymount fell 78-74 at Oregon State on Dec. 2.
Washington: The Huskies were coming off a pair of big games -- an upset of then-No. 2 Kansas on Dec. 6 and a loss to No. 12 Gonzaga on Dec. 10 -- and seemed to struggle with energy at times against the Lions.
Loyola Marymount will finish its non-conference schedule at home Friday against Cal State Fullerton.
Washington plays the third of four straight home games Tuesday against Bethune-Cookman.