Robert Lewandowski scored a hat-trick to help champions Bayern Munich cruise to a 3-0 victory at Schalke 04 on Saturday for their first win in the Bundesliga this season. 

Bayern, who stumbled to a 2-2 draw in their opener against Hertha Berlin, are on four points, two behind leaders Borussia Dortmund, who won 3-1 at Cologne on Friday. 

The 31-year-old Poland forward grabbed his first goal with a 20th-minute penalty and added another with a superbly taken free kick five minutes after the restart. 

He completed his ninth Bundesliga hat-trick in the 75th to take his season tally to five goals in two league matches. 

"I can play even better. I have the potential to further improve," Lewandowski, who is close to signing a contract extension, said, "you can win some matches alone but with the team you win titles." 

"We controlled the match over ninety minutes and neutralized Schalke's actions. We staged overall a faultless performance and played a great game," Bayern's head coach Niko Kovac said. 

For his part, Schalke's head coach David Wagner said, "Bayern grabbed a deserved win here but my team played a good second half. I think we deserved one goal." 

Philippe Coutinho, Bayern's biggest signing for the season, also came on in the second half for his first appearance on German soil after joining on loan from Barcelona. 

For other games, Bayer Leverkusen scored three times in the first half to ease past hosts Fortuna Duesseldorf 3-1 and join leaders Borussia Dortmund with maximum points from their first two matches. 

Freiburg are also on six points after coming from a goal down to beat promoted Paderborn 3-1 while Borussia Moenchengladbach, on four points, did the same for a 3-1 victory at Mainz 05. 

(With input from Xinhua and Reuters)