Borussia Dortmund's shaky win at Wolfsburg on Saturday drew the chasers to within three points but Diaz, unplayable at times, was the difference maker as Bayern delivered an emphatic response.

Harry Kane converted two Bayern penalties, both won by Diaz, to move up to 24 league goals for the season and 38 in all competitions.

Relegation battlers last campaign, third-placed Hoffenheim came to Munich as the Bundesliga's form team, with 11 wins and just one loss in their past 14 games.

The visitors' hopes took an early hit when Kevin Akpoguma was harshly adjudged to have fouled Diaz in the box and saw red.

Kane converted the result spot-kick but Manuel Neuer let Hoffenheim back into the match just minutes later, playing the ball directly to Fisnik Asllani, who squared for Andrej Kramaric to tap home.

Bayern had dropped five points in their past two league games and looked sluggish, other than the energetic Diaz, who earned another penalty after 44 minutes.

Kane stuck it away once more and immediately repaid the Colombian for his generosity, threading a pass on the counter for the former Liverpool man to guide home in first-half stoppage time.

Diaz tapped in a Michael Olise pass midway through the second half to pad Bayern's lead before completing his hat-trick with a shot from outside the box in the final minute.

Diaz's first Bayern hat-trick took his goal tally to 13 in his first Bundesliga season, to go along with nine assists.

Bayern have scored 79 goals in 21 Bundesliga games this campaign.

- Baumgartner brace propels Leipzig -

Earlier on Sunday, goals in each half from Christoph Baumgartner lifted RB Leipzig to a 2-1 win at Cologne and up into fourth.

"It's incredibly tight up there -- we can't afford to make any mistakes," Baumgartner said of the top-four battle."

Stuttgart's loss to St Pauli on Saturday, their first defeat since early December, left the door to the top four ajar and Leipzig obliged, winning for just the second time in five outings.

Austria midfielder Baumgartner has emerged as Leipzig's most potent creative threat since the departure of Xavi Simons to Tottenham in August. He has eight goals and seven assists in 20 league games this season.

The victory will boost Leipzig ahead of their trip to Bayern in the quarter-finals of the German Cup on Wednesday.

The visitors arrived in Cologne in danger of missing Champions League qualification for a second straight season, having picked up just seven points from their past seven games.

Winger Brajan Gruda was named in the starting XI just days after his deadline day arrival from Premier League side Brighton on a six-month loan.

Cologne's teenage winger Said El Mala went close twice in the opening stages but Baumgartner put the visitors in front after 29 minutes, heading in a dipping David Raum free-kick.

Just after the break, Cologne's Jan Thielmann was off balance but somehow managed to stick an impressive shot in the top left corner to level the scores.

Leipzig hit back immediately however, Baumgartner collecting a low pass from Austria teammate Xaver Schlager on the turn before blasting home.