Bayern Munich closed the gap on Bayer Leverkusen at the top of the Bundesliga to a point with a 3-2 victory at Augsburg on Saturday after the hosts endured hit and miss late penalty drama.

Aleksandar Pavlovic and Alphonso Davies put Bayern into a comfortable lead at the break.

Augsburg's Ermedin Demirovic halved Bayern's advantage but Harry Kane struck just before the hour to help secure the three points.

Augsburg then missed one penalty while Demirovic scored from another spot-kick attempt in the final few minutes but Bayern held on for a precious win in one of the closest Bundesliga title races for years.

Xabi Alonso's Bayer Leverkusen, the last unbeaten team in the Bundesliga this season, can re-establish a four-point cushion with victory at home to Borussia Moenchengladbach in Saturday's late game.

Bayern came into this game having got back on track in midweek with a 1-0 win over Union Berlin after a shock 1-0 home defeat by Werder Bremen last weekend.

With Dayot Upamecano limping off with a hamstring injury against Union and joining Bayern's lengthening injury list, Eric Dier made his first start as Davies also returned to the starting line-up after being dropped in midweek.

But it was another player drafted into Thomas Tuchel's starting XI who got things rolling for Bayern.

Making just his fourth start in the league, 19-year-old German midfielder Pavlovic steered the ball in from close range after 23 minutes when Augsburg failed to clear a corner.

Davies let fly from distance deep into first half stoppage time to give Bayern a two-goal cushion.

Demirovic's glancing header early in the second half lifted the mood of the home fans, until Kane tapped in Leon Goretzka's cross.

A clumsy foul by Manuel Neuer saw Augsburg awarded an 88th minute penalty, but the Bayern goalkeeper atoned with a fine save from Sven Michel's spot-kick.

Augsburg won another penalty, in stoppage time, after a trip by substitute Thomas Mueller.

This time Neuer could do nothing about Demirovic's powerful penalty, but it was too little too late for Augsburg.

Bayern keep the pressure on Leverkusen but yet another injury, this time to French winger Kingsley Coman, soured the victory for Tuchel.

In another key game at the top, Deniz Undav scored a hat-trick as Stuttgart thrashed RB Leipzig 5-2 to keep alive their hopes of Champions League qualification.

Borussia Dortmund will have the chance to leapfrog Leipzig and enter the top four with victory over Bochum on Sunday.