TORONTO -- Frederik Andersen's early season woes continued Tuesday night at the hands of Steven Stamkos and the Tampa Bay Lightning.

Stamkos matched a career-high with four points (two goals and two assists) as the Lightning struck with a 7-3 win over the Leafs at the Air Canada Centre. Andersen gave up seven goals on only 24 shots, the third time in five starts that he's allowed at least five goals and fourth time he's allowed four or more.

The 27-year-old is sporting a .851 save percentage so far this season.

Alex Killorn, Victor Hedman, Nikita Kucherov, Vladislav Namestnikov and Jonathan Drouin added goals for Tampa, while Ben Bishop made 40 saves. William Nylander, James van Riemsdyk and Auston Matthews all scored for the Leafs, who mostly outplayed their Atlantic division foes, outshooting them 43-24.

Making his first visit of the season to Toronto after spurning the Leafs in free agency, Stamkos got on the board in his very first shift.

Andrej Sustr intercepted Matthews's failed pass attempt, finding Stamkos in behind the Toronto defence and though the Lightning's captain lost control of the puck, Leafs defenceman Matt Hunwick inadvertently batted it past Andersen.

Stamkos, who re-signed with the Lightning for eight years and US$68 million after flirting briefly with the Leafs ahead of July 1, appeared to get away with a hit from behind on Leafs defenceman Connor Carrick moments before the goal.

Killorn upped the Tampa lead to 2-0 six minutes after the opener on a goal that Andersen would surely like back. The 27-year-old couldn't handle a Braydon Coburn point shot, the attempt slipping through where it was eventually tapped in by Killorn. Andersen had come up with fine stops on Valtteri Filppula and Killorn a few minutes before that, but was unable to maintain those efforts as the period wore on.

Earlier in the day Leafs coach Mike Babcock passionately defended Andersen's play. Babcock pointed to widespread struggles at the position in the opening weeks of October, not to mention the very small sample size.

"Do we think he's played as good as he's capable of playing? No. Do we think he's going to ? Yes," Babcock said. "I think Andersen is going to have a great year this year."

Stamkos rubbed more salt in Andersen's wounds late in the first frame, whistling a perfect one-time shot past beyond the blocker from the top of the faceoff circle. Andersen seemed to think the shot was going to his glove-side as he fought to see it through traffic. It was second goal of the game for Stamkos and fifth already in six games this season.

Bishop, a Vezina Trophy finalist last season, was superb at the other end early in Tuesday's action, stopping quality chances by Leaf rookies Nylander, Mitch Marner and Connor Brown, the latter alone in the slot.

Toronto outshot Tampa 13-9 in the first but trailed 3-0.

The Lightning scored their fourth goal on only their 11th shot, Stamkos driving the action once more. After setting up Hedman on a play that was somehow denied by Andersen moments earlier, Stamkos fired a pass into the slot. The deflected puck eventually made its way to Hedman, who tucked in his first goal this season.

Andersen wasn't helped at times by the occasional glaring error of his teammates, such as the giveaway by Matthews and on the fourth goal, too, Hedman somehow slipping unnoticed to the net front. He's also playing as an undisputed No. 1 goaltender for the first time, signing a rich five-year deal with Toronto following a summer trade from Anaheim.

The NHL's only Danish netminder looks rattled though from the early shelling.

It was Bishop who suffered some pain later in the second frame when a Peter Holland shot hit him straight in the mask. The American goaltender fell immediately to the ice and lost teeth on the play. He searched the ice with teammate Brian Boyle, who eventually seemed to locate the lost ivories.

Bishop remained in the game, yielding a late period power-play goal to Nylander.

The 20-year-old was fed perfectly on the play by Nazem Kadri, depositing his fourth goal and eighth point already this season. Nylander, who added a third period assist, has eight goals and 20 points in his last 18 NHL games and at least a point in five of six games this fall.

Kucherov, Namestnikov and Drouin added third-period goals for Tampa in a third period dominated by the Leafs (shots were 17-9). van Riemsdyk and Matthews both scored just over a minute apart, but the late rally ultimately fell short.

Matthews now has 10 points in his first six NHL games, vaulting into first in the overall scoring lead with Tuesday's performance.