Matthews scored on the power play at 19:25 of the first period to give the Maple Leafs a 1-0 lead. He took a pass from John Tavares on a scramble in front of the net for his 19th goal of the season.
Wayne Simmonds made it 2-0 at 8:47 of the second period. He kicked the puck up to his stick in front and swept it in past Koskinen.
Edmonton has trailed 2-0 in five straight games.
"I think we started really well. We had a game plan to be aggressive and go straight ahead and I thought we did that for the most part in the first period and it led to some really good chances for us," Oilers associate coach Jim Playfair said.
"I thought we continued that mindset in the second, but coming out of the first with a goal being scored against us … that puts you behind the eight ball and now you're chasing a little bit and we've done that, as we all know, too often lately."
TJ Brodie scored at 14:54 for a 3-0 lead. His point shot deflected in off McDavid's stick.
Colton Sceviour scored his first with Edmonton at 5:26 of the third period, sweeping in a shot from the left side of the net to make it 3-1. It was his first goal in 32 games; the last coming April 11, 2021, when he was with the Pittsburgh Penguins.
"I thought our guys did a really good job of capitalizing on our chances, making good on them and I thought we played a really disciplined game defensively," Maple Leafs coach Sheldon Keefe said. "At times, we defended more than we would like, but I thought we did a good job of doing the things we were looking to do before the game, which was to limit the space and speed of their best people."
Rielly converted a centering pass by William Nylander from behind the net at 6:33 to make it 4-1, and Matthews scored on a shot from the slot at 16:40 for the 5-1 final.
Edmonton outshot Toronto 24-13 in the final two periods.
"I think the most frustrating part of the whole thing is that if you look at the last three or four games, we played in stretches better than the teams we were playing against," Sceviour said. "Then when we gave up opportunities, we gave up Grade A-pluses and I think that's probably the thing we need to get over the most. Some of those chances we're giving up, you can't afford to give them up against good players in the NHL, because they're going to end up in the back of your net."