Rielly scored off a shot from the point to make it 4-3 at 10:01, and Matthews extended the lead to 5-3 at 10:56 on a turnaround in the slot that beat Golden Knights goalie Marc-Andre Fleury blocker side.
"Close game going into the third, they score a big goal. I thought we responded well," Rielly said. "This is a pretty cool place to play, pretty cool building to play in. We were excited to come here. Obviously, we're happy with the result, but there are little things over the course of the game that we can take away as good signs and we're looking forward to keeping this road trip going and hopefully we can keep playing well."
WATCH: [All Maple Leafs vs. Golden Knights highlights]
Mitchell Marner scored a shorthanded goal on a 2-on-1 at 16:33 to make it 6-3.
Matthews had two goals and an assist, Marner and Rielly each had a goal and an assist, and Kasperi Kapanen and Jake Muzzin each had two assists for Toronto (36-18-3), which has won two in a row and is 7-1-1 in its past nine games. Frederik Andersen made 30 saves.
"We drew a lot of penalties tonight (2-for-6 on power play)," Matthews said. "We started off terrible and we were able to get one early, but it still wasn't clicking well. We're a good, fast team drawing penalties and we've to be able to capitalize on the power play."