Jones made 22 saves for the Sharks (36-23-9), who are in second place in the Pacific Division, one point ahead of the Anaheim Ducks and two ahead of the Los Angeles Kings. San Jose trails the Vegas Golden Knights by 12 points.
"It was one of those games we never really got our momentum going," Sharks captain Joe Pavelski said. "It was a couple turnovers early, and we break out, get going a little bit then revert back. That's just part of how hockey is right now. I don't think they had a ton of chances. We have to realize we've got to keep sticking it in. We were one shot off from tying that game."
Backstrom made it 1-0 at 18:32 of the second period with a slap shot from the left circle to the far side. Lars Eller scored into an empty net with 1:49 remaining in the third period to make it 2-0.
"It was nice to see it go in," Backstrom said. "Two good goaltenders out there. You know it's going to be this kind of game, playoff game kind of, a lot of back and forth. Also nice to get the [win]."
Washington won the finale of its California road trip after losing to Anaheim 4-0 on Tuesday and to Los Angeles 3-1 on Thursday.
"It was a really solid game," Trotz said. "Just look at this whole road trip. Take away maybe that first period in Anaheim, we played pretty well, we just didn't get the results. Today was really solid. The first two periods were as good as you're going to get from us. We didn't give them anything."