Max Jones scored Anaheim's lone goal, breaking Cam Talbot's shutout bid with 2:50 to play in regulation. Anthony Stolarz made 28 saves in his fifth start of the season.
Five different Senators, including Brassard and Joseph, scored in the win, which snapped a three-game losing skid for the visitors. Brady Tkachuk, Tim Stutzle and Artem Zub also scored. Drake Batherson tallied two assists.
Talbot earned his second win as a Senator, stopping 30-of-31 Anaheim shots. The 35-year-old veteran, now with his sixth NHL team, owns a 15-7-2 all-time record against the Ducks.
Two days after Anaheim went 4-4 on the penalty kill against New York, Ottawa's power play proved the biggest difference in the game, burning Anaheim for three power-play goals.
Anaheim played a strong first period, outshooting Ottawa 13-7 in the opening frame, but it would be the Senators taking a 2-0 lead back to the locker room in part thanks to special teams success.
Tkachuk opened the scoring on a late period power play, converting a crisp tic-tac-toe passing play from the low slot.
The Ottawa captain paces the team in scoring (8-15=23) and assists, and co-leads in goals.
The Sens struck again just 1:55 later on another well-executed passing sequence, this time with Brassard finishing off a four-on-three rush by tapping in a backdoor dish from Joseph.
The Ducks would also get their opportunities on the man advantage early, as the Senators took three minor penalties in the initial 20 minutes, but Anaheim was unable to cash in on those opportunities despite some close calls at the Ottawa net.
It would be a similar story in the middle frame, with near-misses on one end soon giving way insurance goals on the other.
Stutzle, the third overall pick in the 2020 draft, pushed the lead to three with another power-play goal, taking a pass in the middle of the ice and beating Stolarz to the glove side.
The German-born Stutzle has points in three straight games (2-1=3) and 20 points in as many games this season.
The Ottawa hit lead four less than five minutes later when Zub got a point shot through traffic, sneaking it over Stolarz's glove before the Anaheim netminder could find the puck amidst a screen in front.
Joseph capped the scoring with a third-period power-play marker, the second such goal of his 251-game NHL career.
Anaheim nearly got on the board on a late third-period power play when Mason McTavish hammered a one-timer from Trevor Zegras in the right circle, but the bid rang the nearside post and stayed out.
The Ducks would finally break through and beat Talbot moments later on a relentless effort by Jones in the Ottawa crease. With a loose puck free around Talbot, Jones went wacking away at it through two defenders, eventually getting just enough to push it over the line.
