Vladislav Namestnikov, Brady Tkachuk and Nick Paul each scored for the Senators, who opened a season-high six-game homestand by ending a four-game skid (0-2-2) at home.
Oliver Ekman-Larsson and Jordan Oesterle scored for the Coyotes, while Antti Raanta stopped 28 shots.
Arizona wrapped up its four-game road trip Thursday with a 1-2-1 record. The Coyotes, who host Washington on Saturday, are in a tight playoff race in the Pacific Division and hope to gain ground on Calgary and Vegas.
''We can't look too far ahead,'' Ekman-Larsson said. ''We've got to look at the next one here on Saturday, I believe. On Saturday, we've got to get some wins together at home and play better and go from there.''
Hogberg preserved Ottawa's 2-1 lead by starting off the third period with two saves on Lawson Crouse.
Paul then gave the Senators a two-goal advantage as Raanta got a piece of his snap shot, but it got past the Arizona goalie and dropped into the net. The goal was Paul's first since Dec. 30.
''There's very few games this year he hasn't had good legs,'' Ottawa coach D.J. Smith said. ''He's a dependable guy that can play in all situations. ... He's playing every game to stay in the league and those are the hungry guys you want on your team.''
The Coyotes battled back as Oesterle beat Hogberg five-hole two minutes later, but Arizona couldn't get the equalizer.
''A couple games, we've kind of left him out to dry at the start,'' Tkachuk said. ''We wanted to put the pressure off him and try to get pucks behind and be physical and try to create turnovers, and I thought we did that pretty well in the first and a little in the second.''
Hogberg was spectacular for Ottawa in the second period, making great saves on Vinnie Hinostroza and Nick Schmaltz. Arizona was finally able to beat him with a power-play goal late in the period.
Ekman-Larsson took a feed from Taylor Hall and put a shot through traffic that took a bounce off Namestnikov on its way to the net.
Hogberg said he has had frequent chats with goalie coach Pierre Groulx ''to try and be more calm and don't move too much.'' Hogberg added: ''I think that's helping me a lot.''
The Senators, who were 0-4-2 in their last six, got the start they were looking for as they took a 2-0 first-period lead.
Ottawa opened the scoring just 2:50 into the first period as Drake Batherson chased down a dumped puck and dropped a pass back to Namestnikov, who beat Raanta from in close.
Tkachuk made it 2-0 as he tipped Thomas Chabot's point shot for his 17th of the season.
''Not ready to go, my fault,'' Coyotes coach Rick Tocchet said. ''The game plan was there. Ottawa likes throwing pucks to the net and we just didn't box out. I thought (Raanta) could have helped out on the dump in on the first one, but saying that, we were chasing the game after that.''
NOTES: Ottawa's Tyler Ennis played in his 600th career game. ... Mark Borowiecki returned to the Senators' lineup after missing the last two games for the birth of his son Miles. But, Borowiecki was injured during Paul's goal when he collided near Ottawa's bench and hobbled off the ice. Smith said there was no fracture, but added that Borowiecki would likely be ''out some time.''
Coyotes: host Washington on Saturday night.
Senators: host Toronto on Saturday night.
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