Bayern Munich followed up the qualification for the Champions League semi-finals with a 5-1 thrashing of Union Berlin, while Cologne sank even further into the Bundesliga relegation zone after they were stunned at home 2-0 by Darmstadt on Saturday.
Coming off a 1-0 mid-week win against Arsenal, Bayern had a slow start but were ahead in the 29th thanks to Leon Goretzka.
Union seemed close to an equalizer and goalkeeper Manuel Neuer had rescue Bayern twice, but it was the guests again to find the net with a stunning free-kick from Harry Kane shortly before the break.
Goals from Thomas Müller and Mathys Tel put the game to bed already in the 62nd, before Müller completed a brace in the 66th to celebrate his 400th start in the Bundesliga.
Union, however, didn't let Bayern go back home with a clean sheet and got their consolation goal in stoppage time.
Müller's first goal marked a curious milestone: It was the first time the Bayern veteran scored in matchday 30.
"An incredibly important statistic. Of course, it was very important for me to score today at all costs," Müller joked.
Bayern sit second with 66 points. After they had their 11-year dominance in the league ended by Bayer Leverkusen last weekend, Bayern's goal this season is to qualify for the Champions League.
With four games left, they are seven points ahead of RB Leipzig, who currently hold the last spot for the top competition.
"We're happy, it was a perfect week for us. It is not a given to win here in this way after the difficult game we had mid-week. Compliments to the team. It was a team effort," coach Thomas Tuchel said.
Bottom club Darmstadt found the breakthrough in the 57th after Cologne failed to deal with a corner. The ball fell to Christoph Klarer, who fired his shot between the legs of a defender and goalkeeper Marvi Schwäbe. Oscar Vilhelmsson scored in stoppage time to put the game to bed.
Cologne are five points from Bochum, the first team out of the danger zone, and staggering towards their seventh relegation from the Bundesliga since 1998.
"We know that the situation is tense. It was also an absolute shit afternoon for us," defender Timo Hübers said.
RB Leipzig scored a late goal in a 2-1 win against Heidenheim as they bid to qualify for the Champions League. Nikola Dovedan cancelled out Benjamin Sesko's opener in the 69th, but Leipzig claimed the win in the 85th thanks to Lois Openda.
"It was a difficult away game, as we expected. Congratulations to Heidenheim. They're doing really well this season. We had to work hard today," Leipzig coach Marco Rose said.
Leipzig are fourth, currently the last spot for next season's Champions League, and three points ahead of fifth-placed Borussia Dortmund, who host newly-crowned champions Leverkusen on Sunday.
"Next week we have a 'big-point game' against Dortmund at home, that will be fun," goalkeeper Peter Gulacsi said.
The Bundesliga, however, is closing in on a fifth Champions League spot, with ruling body UEFA awarding the top two nations in its events this term with an additional slot. Germany are currently second in the UEFA season rankings.
Wolfsburg, meanwhile, took a breather and increased their gap to the drop zone thanks to a 1-0 win against Bochum.
Bochum were denied a breakthrough in the 39th after a video review spotted goalscorer Patrick Osterhage in offside position. Wolfsburg then took the lead just four minutes later with Jonas Wind, who scored his first Bundesliga goal since November.
Elsewhere, Hoffenheim claimed a 4-3 stoppage-time win in a thrilling home match against Borussia Mönchengladbach.
Robin Hack put Gladbach level just three minutes after Wout Weghorst scored Hoffenheim's opener in the 36th. But Grischa Prömel and Ozan Kabak hit the net in second half to give the hosts a safe 3-1 lead.
The visitors, however, hit back as Robin Hack completed his hat-trick with two late goals, but Anton Stach had the final word in stoppage time to give Hoffenheim the three points.
