Cologne eased their Bundesliga relegation fears on Sunday with a 3-1 home win over 10-man Werder Bremen, who remain three points above the danger zone.
VfB Stuttgart meanwhile moved above RB Leipzig into third place on goal difference with a 4-0 home romp over SV Hamburg.
In the late game, Freiburg won 1-0 at mid-table Mainz thanks to Lucas
Höler's header as the eighth-placed side look for another European berth through the Bundesliga or by lifting the Europa League.
Cologne's victory was their first in nine matches and first under interim coach René Wagner after last weekend's 2-2 draw at Eintracht Frankfurt in his opening game in charge.
Saïd El Mala netted his first top-flight penalty for the Billy Goats early on after Olivier Deman fouled Jakub Kamiński. The Germany under-21 winger has 11 Bundesliga goals this season after a third in four games.
"The three points have done wonders for the whole squad. We deserved it," the 19-year-old told DAZN. "We played the better game."
Things got worse for Bremen midway through the first half when skipper Marco Friedl was sent off for a professional foul and the visitors barely threatened thereafter.
Cologne made it 2-0 through Ragnar Ache on 65 minutes but the striker later conceded a spot-kick which Romano Schmid converted. Ísak Jóhannesson secured Cologne's victory in stoppage time, with the goal later being given as an own goal by keeper Mio Backhaus.
Bremen host not-yet-safe Hamburg in a crucial northern derby next Saturday without their captain in an already injury-hit defence.
Home side Cologne leapfrogged fourth-bottom Bremen and now sit five points clear of the relegation play-off spot and nine above the automatic drop zone, occupied by Wolfsburg and Heidenheim.
Hamburg swept aside by Stuttgart
In Stuttgart, Germany World Cup hopefuls Angelo Stiller, Chris Führich and Maximilian Mittelstädt scored to put the hosts four points above fifth-placed Bayer Leverkusen, who won at Borussia Dortmund on Saturday when Leipzig edged Borussia Mönchengladbach.
Deniz Undav blazed over a late penalty before Bilal El Khannouss added the fourth with a deflected effort.
The Bundesliga is behind Spain in the race for a fifth Champions League berth next term and may have to settle for four, making Stuttgart's win over Hamburg all the more important with five games to go.
Stuttgart coach Sebastian Hoeness said: "We played really well. We managed to play with intensity from the start and for long stretches we also defended resolutely and clearly.
"It's curious that we won 4-0 and still have the feeling we could have scored one or two more goals. That sums up how convincing the performance was."
On Saturday, Stuttgart's next opponents Bayern Munich broke the Bundesliga season goals record (now 105) and moved within four points of retaining their title with a 5-0 triumph at third-bottom St Pauli, who are languishing in the relegation play-off place.
The other big news of the Bundesliga weekend was mid-table Union Berlin's decision to sack Steffen Baumgart and appoint Marie-Louise Eta until the end of the season, making her the first woman to solely coach a men's team in Europe's top five leagues.