Bundesliga top scorer Harry Kane netted a penalty to give Bayern Munich a 1-0 victory at Borussia Monchengladbach on Saturday in their first league match after the winter break, keeping them four points clear of second-placed Bayer Leverkusen.

The England captain sent Gladbach keeper Moritz Nicolas the wrong way in the 68th minute to break the deadlock and bag his 15th league goal this season.

Despite Bayern's victory, head coach Vincent Kompany said his side should have scored several more goals and killed off the game much earlier.

"It is a very difficult away game and we were just back from holidays," Kompany told a news conference. "If you had the chances we had today you would want to score two or three goals to kill off the game. We never did that."

Bayern had control of the game with some 70% possession in the first half but struggled to convert that to goals after going close through Thomas Müller and Leon Goretzka.

The Bavarians, who had several more chances to score after Kane's penalty, are in top spot on 39 points, with champions Leverkusen in second place on 35 after Friday's 3-2 win at Borussia Dortmund.

It was one-way traffic from the start with Bayern having control of the game.

The home side were content to sit back and soak up the pressure, having no effort on or towards goal in the entire first half, and leaving Bayern keeper Manuel Neuer, making his comeback after a month-long injury absence, with little to do.

Gladbach's Tim Kleindienst almost struck four minutes after the restart but his header at the far post flew narrowly over the bar.

But it was Kane who scored when he converted the spot kick following a foul on Michael Olise in the box.

Vincent Kompany's team should have scored again late in the game but neither Alphonso Davies nor Serge Gnabry could beat Nicolas.

"What I liked was the attitude and mentality to keep fighting," Kompany said. "In the final 10 minutes things could still happen but we kept our cool.

"We could again have scored a few more goals but the concentration of the team was really good."

Gladbach dropped to 10th place following their first home game this season in which they failed to score.