It was Hogberg's first start since April 7 and first win since Feb. 15.
"That's [Hogberg's] best game of the year, for sure," Ottawa coach D.J. Smith said. "Didn't have a lot of action in the second but made big saves."
Brady Tkachuk had two assists for the Senators (18-27-4), who are 4-1-0 in their past five games. Ottawa has won two of three in the four-game set with the Canucks, which concludes Wednesday.
"It's been a blast, not just learning how to win, but learning how to win against a desperate team who needed these points to stay in the playoff race," Tkachuk said. "I think our team is learning so much through this experience. It's definitely a better atmosphere and more fun when we're winning."
Olli Juolevi scored, and Braden Holtby made 25 saves for the Canucks (19-20-3), who lost for the second time in eight games against the Senators this season.
"It's a fine line at this time of the year between winning and losing," Vancouver coach Travis Green said. "I thought we made a couple of mistakes that we'd like to have back. We talk to our team a lot about how every shift matters, especially at this time of the year. Every turnover, every puck battle matters. I thought we let our foot off the gas, defended a little slow in the second. We made a couple of soft plays on the wall and we lost the momentum for about 7-10 minutes."