Leaders Bayern, who hold a one-point lead at the top, remain the favourites after thrashing Schalke 6-0 at the Allianz Arena with Serge Gnabry grabbing two of their goals.
Dortmund kept up the fight with a 5-2 home hammering of Monchengladbach.
Donyell Malen pounced to put them ahead before Jude Bellingham added a penalty and Sebastian Haller struck twice. Gio Reyna wrapped up the scoring after Gladbach pulled a couple back with a Ramy Bensebaini spot-kick and Lars Stindl effort.
Kylian Mbappe scored twice after goals from Fabian Ruiz and Achraf Hakimi had put PSG in command. The scoring was completed with a Mohamed Youssouf own goal but both sides ended with 10 men after Hakimi and Thomas Mangani were sent off late on.
The victory lifted PSG six points clear of second-placed Lens with three games remaining.
In Italy, AC Milan’s hopes of a top-four spot suffered a blow as they slumped to a 2-0 loss at relegation-threatened Spezia.
Both goals came in the closing stages with Przemyslaw Wisniewski opening the scoring after 75 minutes and Salvatore Esposito adding a free-kick 10 minutes later.
Inter, meanwhile, moved up to third with a 4-2 win over Sassuolo.
Inter had led 3-0 after an hour following Lukaku’s opener, a Ruan own goal and Lautaro Martínez strike.
Real Madrid made eight changes for their derby against Getafe but still did enough to claim a 1-0 win that lifted them back to second in LaLiga.
Karim Benzema and Rodrygo were among those to get a night off ahead of the second leg of their Champions League semi-final against Manchester City while Luka Modric and Vinicius Junior came off the bench.
Marco Asencio scored the only goal of what was a comfortable win at the Bernabeu.