Robert Lewandowski scored a hat trick and Philippe Coutinho made his debut as champions Bayern Munich cruised to a 3-0 victory at Schalke on Saturday for their first win in the Bundesliga this season.

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.

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.

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

"The Bundesliga is no easy league and that is why we constantly have to be ready. I was ready and happy to have helped the team," he said.

The striker has now converted 24 of his 27 Bundesliga penalties while also scoring 16 goals in 19 league matches against Schalke.

His second goal looked to be a wake-up call for Schalke who grabbed control of the game and were unlucky not to be awarded a penalty for a handball by Bayern's new signing Ivan Perisic.

Their revival was short-lived, however, and Lewandowski put the game beyond them when he controlled the ball at the edge of the box before completing his hat trick with a clinical finish.

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 and told reporters he was honored to play next to a "legend" like Lewandowski.

"It's amazing to play alongside him. He's a legend," Coutinho said. "He's a great player, a great guy. I have been here for three or four days, and I saw his qualities right in the training. Today, he scored a hat trick."

In his first 30 minutes of Bundesliga football, Coutinho added up 36 touches and played 28 passes from his position in Bayern's central midfield.

In front of his family attending the match at the sold-out Veltins Arena, he came close to a flying start in Bundesliga after Lewandowski set him up with a through ball, but Schalke keeper Alexander Nubel rushed out of his goal to reach the ball before Coutinho.

Still, he was delighted and said: "It was amazing. I was looking forward to my first match here. And the stadium was full. I am just very happy."

Reuters and ESPN FC correspondent Stephan Uersfeld contributed to this report.