John Tavares also scored for the Maple Leafs, who won the first two outings in a three-game California road trip. Goaltender Martin Jones made 27 saves to net his second victory in as many nights.
Anaheim goaltender Lukas Dostal stopped a franchise-record and career-best 55 shots - 21 in the third period - in a brilliant performance.
The Maple Leafs' 57 shots were tied for their most on the road since NHL shot tracking began in 1959-60.
Frank Vatrano scored for the Ducks, who have managed only one win in six games (1-4-1) to kick off an eight-game homestand, and have only four victories in 22 outings (4-17-1) dating back to November 15.
On the decisive goal, Matthews converted a one-timer set up by Mitch Marner at 2:12 of overtime for his first game-winning goal of the season and 30th of the campaign.
Dostal and the Ducks led with less than six minutes remaining.
Vatrano broke the scoreless deadlock at the 11:41 mark of the second period with his team-leading 18th goal, a shorthanded backhand shot from the doorstep.
The Maple Leafs finally tied the score when Tavares pounced on a rebound for a power-play goal with 5:43 remaining in regulation, his 12th of the campaign.
It was Toronto's 50th shot of the game, and spoiled Dostal's heroics.
After a quick Anaheim early push, the Maple Leafs outshot the Ducks 18-9 in the first period, but couldn't light the lamp. And when Dostal was not making the save, he received help, notably when Ilya Lyubushkin swept away the puck from the goal line when Matthews figured he had opened the scoring with an open net to slip the puck into it.
Dostal was a human highlight reel onward. In the second period, he had Toronto's Matthew Knies looking skyward on more than one occasion. In the third period, Nylander was denied on a partial breakaway midway through the frame, which was followed by a series of stops on Matthews before the Maple Leafs finally found the mark.
When the final buzzer sounded, Matthews fired 13 shots on goal, while Nylander registered eight shots and both Marner and Tavares sent seven shots on net.
