Brady Tkachuk scored, and Murray made 26 saves after missing two games with an upper-body injury for Ottawa (4-13-1), which had won two in a row.
"That's a game that could have gone either way against a very good team, so I was proud of that effort," Murray said.
The Senators outshot the Maple Leafs 10-5 in the first period. Matthews credited Andersen for getting Toronto out of the period without allowing a goal.
"He's just so composed in there all the time," Matthews said, "Tonight early on, when we needed some saves, he came through with some big saves for us and kept it a 0-0 game. He does that on a nightly basis for us."
Thornton had two goals disallowed: the first with two seconds left in the first period when it was ruled he pushed Murray's right pad into the net; the second at 4:32 of the second period when he deflected Muzzin's point shot with a high stick.
The Maple Leafs took a 1-0 lead at 4:41 of the second period when Matthews one-timed a shot from the right face-off dot after taking a pass from Justin Holl.
Matthews leads the NHL with 14 goals and has 20 points in his streak.
"There's probably two or three guys I've played with that could do what he does, but he's on another level," Thornton said of Matthews. "He just competes so hard. I think he should be up for Selke, Hart, Rocket Richard trophies. He just does so many things and just plays the game the right way. I really enjoy watching him and playing alongside him. He's the complete package."
Tkachuk tied it 1-1 at 18:51 when he deflected a pass from Chris Tierney at the top of the crease. It was Tkachuk's 100th NHL point.
"Very good (road) game, I thought the chances were probably even," Ottawa coach D.J. Smith said. "We got into some penalty trouble and we didn't make some plays in the third period we should have made. And then we got hemmed in our zone. I thought we did a lot of great things. I thought we broke the puck out well. We skated. We had our chances. Maybe it's 2-1 on the night, but it could go either way."
NOTES: Matthews missed a 4-2 win at the Edmonton Oilers on Jan. 22 and has 16 points (12 goals, four assists) in an 11-game point streak since. … Muzzin had two assists to give him 200 in the NHL in 596 games. … Tkachuk has 48 goals and 52 assists in 160 NHL games. … Senators defenseman Erik Brannstrom had four hits playing 14:18 after missing four games with an undisclosed injury.