Drake Batherson scored for Ottawa (16-22-7), who have lost seven straight (0-4-3), including 3-2 to the Detroit Red Wings in a shootout on Friday.
"We played real hard," Senators coach D.J. Smith said. "For a back-to-back, a little sluggish in the first, and then we really started to skate from there. We had some opportunities in the second period, pucks kind of bobbled on us. We had some opportunities in the third, Price made some big saves. And [Marcus Hogberg] was outstanding for us."
Hogberg made 23 saves, starting his second game in a back-to-back.
"Some nights it's harder when you don't get that many shots from the beginning," Hogberg said. "You have to be ready all the time, be aware that the game can be quick."