Lewandowski produced the first chance of the game from an early free-kick, but the resulting shot was comfortably dealt with by Schalke's Alexander Nubel.

He returned with a second, more probing effort shortly afterwards, connecting with a header from summer signing Benjamin Pavard and this time provoking a brilliant save from Nubel to keep the score line level.

Liverpudlian right-back Jonjoe Kenny then handed Bayern a penalty by bringing down French forward Kingsley Coman, with Lewandowski stepping forward to calmly convert the opportunity and give the Bavarians the lead.

Schalke had a slight chance before the break, when Austrian striker Guido Burgstaller cut through on the right, but the threat was eventually diffused by centre back Niklas Sule.

A second Lewandowski goal then came from a long-distance free-kick, with the striker curling the ball over the wall and leaving Nubel unable to block what was a superb shot.

Newly signed duo Perisic and Coutinho both stepped on to the pitch after the break, having recently joined the club on loan deals from Inter Milan and Barcelona respectively.

The hosts seemed to be finally hitting their stride with a handful of late chances, but they were repeatedly denied a life line by a dominant Bayern side who had victory in their sights.

Lewandowski then made his side unassailable in the 75th minute, picking up a cross from Coman and easing past Salif Sane before firing a low shot into the near corner to round off a commanding victory for the Bavarians.

Schalke's loss means they are yet to prevail in an encounter with Bayern since last beating them in 2010, having lost 15 of the last 18 clashes between the two sides and drawn the other three.

David Wagner, appointed soon after his Huddersfield exit, began his reign at Schalke by gaining a point from a goalless draw at Borussia Monchengladbach, but was unable to produce any sort of challenge to Bayern's supremacy.