Carrick fired his dragging wrist shot through a crowded crease and past Ottawa goalie Craig Anderson for the decisive strike with 11:02 remaining in the game. It was Carrick's third goal of the season.
Zach Hyman, Auston Matthews and Mitch Marner each scored a goal for Toronto, which snapped its season-high four-game losing streak (0-1-3) and avenged Wednesday's 4-3 loss to the Senators.
The Maple Leafs had lost four straight against Ottawa and were 1-6-3 in the past 10 meetings.
Frederik Andersen made his ninth straight start and stopped 15 shots for Toronto.
Erik Karlsson, Mike Hoffman and Tom Pyatt scored for Ottawa -- all in the second period -- and Anderson stopped 29 of 33 shots as the Senators lost their second straight after Thursday's 4-1 loss to St. Louis.
The Senators have dropped three of their last four and fell to 3-3-1 in 2018.
Hyman fought through chaos in front of the net and slipped the loose puck past Anderson to put the Maple Leafs ahead 1-0 with 12:34 left in the first period.
Karlsson, who missed practice Friday with an illness but was healthy enough to play, tied the game at 1-1 with a wrist shot from the right circle during a power play only 3:08 into the middle period.
Hoffman's goal came just over four minutes later to put Ottawa in control. After taking a feed from Cody Ceci on a rush, Hoffman beat Andersen stick side with his wrister.
Pyatt tacked on his sixth goal of the year while shorthanded with just under two minutes to play in the second, giving Ottawa a two-goal cushion.
Matthews lit the lamp for his 20th goal just 2:53 into the third before Marner's sixth tally tied it at 4:21 on the power play.
Despite being a game-time decision, Toronto's Morgan Rielly missed the game with an upper-body ailment he sustained Thursday against Philadelphia. Ottawa third-liner Nate Thompson also sat out with a lower-body injury.
Toronto breaks up a stretch of four out of five games on the road with a home tilt against Colorado on Monday. Ottawa begins a quick two-game road trip Monday in Minnesota.
--Field Level Media
Toronto | Ottawa | |
Jake Gardiner 3 | Points | Mark Stone 2 |
Zach Hyman 1 | Goals | Mike Hoffman 1 |
Jake Gardiner 3 | Assists | Mark Stone 2 |
Mitchell Marner 1 | Power Play Goals | Erik Karlsson 1 |
N/A | Short Handed Goals | Tom Pyatt 1 |
Frederik Andersen .833 | Save Percentage | Craig Anderson .879 |
Frederik Andersen 15 | Saves | Craig Anderson 29 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Toronto | 33 | 4 | 1-3 | 1-2 | 6 | 36 |
Ottawa | 18 | 3 | 1-2 | 2-3 | 8 | 34 |