Ilya Kovalchuk scored his NHL-leading 20th goal 16:20 into the second, breaking an offensive drought for Atlanta that lasted seven-plus periods and covered 166 minutes.
In losing their third straight, the Thrashers never really threatened Toronto, which scored four goals for the first time in 14 games.
"We don't just expect Kovalchuk to score," Thrashers center Bobby Holik said. "We expect all of us to score."
For the Maple Leafs, the pregame situation was arguably more desperate.
Not only had Toronto struggled on the ice, but Maurice also had to listen to reports out of Canada saying that general manager John Ferguson wanted to fire him and that Leafs president Richard Peddie might fire Ferguson.
Maurice sidestepped a question, however, when asked what he'd like to tell Ferguson after the victory.
"Congratulations," Maurice said with a deadpan smile.
Sundin, 26th in NHL history with 536 goals, put the Leafs up 2-0 with a backhander from the left circle that beat goalie Johan Hedberg to the stick side.
"We had scoring chances from all four lines," Sundin said. "All around, I felt we had a good effort from our club. There's no doubt we need to put a few wins together."
Antropov earned his 13th assist on Andy Wozniewski's bizarre goal that opened the scoring with 5:50 left in the first. Wozniewski might want to credit Hedberg, who inadvertently knocked in the puck with the back of his left glove.
Regardless, Wozniewski raised his arms in triumph after watching his shot sail over the net, ricochet off the rear boards and bounce off the goalie. Hedberg was in the crease and facing forward with the back of his skates at the goal line when the puck went into the net.
"For me, it was a high stick when Antropov knocked it over the net," Hedberg said. "He [hit] it with the stick. I was waiting for the high stick [call]."
Alex Steen's fourth goal gave the Leafs a 2-0 lead with four seconds left in the first and ended a personal 11-game scoring drought. Matt Stajan hadn't scored in his last 10 games before his fifth goal put Toronto ahead 4-1 with 13:56 remaining.
"We don't let the pressure bother us," Steen said. "We want to be a playoff team and want to play good hockey. We're going to try to get a winning streak started."
Tobias Enstrom's third goal for Atlanta, coming on the power play with 7:29 left in the game, made it 4-2.
Leafs goalie Vesa Toskala improved to 7-8-3 after stopping 18-of-20 shots. Hedberg made 21 saves.
Toronto, which had lost seven of eight, will try on Saturday against Pittsburgh to win consecutive games for the first time since taking two straight from the Penguins and New York Rangers on Oct. 25-27.
Though it's too early to say the Leafs are playing smarter, Maurice likes what he's seen recently.
"I think in the last two or three games, the team has started to make passes in the neutral zone," Maurice said. "Overall, our defensive zone coverage is much more solid. I thought we did a pretty good job of keeping Atlanta to the outside."
Sundin needs five goals to pass Teemu Selanne for 25th place on the NHL's career list. ... Atlanta has earned just eight points at Philips Arena this season. ... Despite the Thrashers' recent offensive problems, Kovalchuk has 12 points, including six goals, in his last seven games.
Copyright by STATS LLC and The Associated Press
Arena: Philips Arena Location: Atlanta, Georgia
Referees: Stephane Auger, Dave Jackson Linesmen: Lyle Seitz, Anthony Sericolo
Attendance: 14,031 (75.7% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Andy Wozniewski (2)
Assists: Jason Blake, Nik Antropov
Alexander Steen (4)
Assists: Kyle Wellwood, Hal Gill
Mats Sundin (13)
Assists: Nik Antropov, Mark Bell
Ilya Kovalchuk (20)
Assist: Niclas Havelid
Matt Stajan (5)
Assists: Boyd Devereaux, Hal Gill
Tobias Enstrom (3)
(Power Play) Assists: Marian Hossa, Darren Haydar