Boston lost at Utah on Tuesday, 96-91, for its seventh defeat in nine games.
Paul Pierce, who contributed 24 points and eight rebounds, gave the Celtics an 88-86 lead with a 3-pointer with just under three minutes remaining, but they were blanked thereafter until the final seconds.
The Warriors opened their trip with a 124-103 loss to the league-worst Cleveland Cavaliers on Tuesday.
Golden State, which is 3 1/2 games behind Houston for the eighth and final Western Conference playoff spot, also faces playoff-bound teams Philadelphia, New Jersey and Portland on its trip.
Boston beat Golden State in Oakland on February 18, 125-117.