Bayern Munich fought back from three goals down to clinch a 4-3 win over Mainz 05 as substitutes Harry Kane and Michael Olise led a second-half comeback for the Bundesliga champions. Dominik Kohr, Paul Nebel and Sheraldo Becker scored for Mainz in the first half while Bayern, who had made eight changes to the starting lineup that beat Bayer Leverkusen in Wednesday’s German Cup semi-final, had no shot on target until the break.

The Bayern coach, Vincent Kompany, brought on Kane and Olise after the break and their renewed aggression paid off with Nicolas Jackson scoring in the 53rd minute and Olise finding the net 20 minutes later.

Jamal Musiala scored the equaliser for Bayern in the 80th minute, and Kane, the league’s leading scorer, netted his 33rd goal in the campaign three minutes later to seal his team’s ninth straight win in all competitions.

Barcelona continued their march towards the La Liga title with a 2-0 victory at Getafe as goals from Fermin Lopez and Marcus Rashford secured a ninth consecutive league win.

Marcus Rashford scored Barcelona’s second goal against Getafe. Photograph: MARISCAL/EPA

The result moved Barcelona to 85 points, 11 ahead of second-placed Real Madrid with five rounds remaining, after Real’s 1-1 draw at Real Betis on Friday.

The breakthrough arrived for Barcelona just before the interval as Lopez latched on to a Pedri through ball, charging into the area to steer a clinical finish into the bottom corner.

Barcelona secured the points in the 74th minute after a clinical counterattack initiated from a Getafe throw-in deep in the visitors’ half. Rashford collected the ball on the halfway line and drove forward largely unchallenged before dispatching a composed, low strike from the edge of the penalty area.

Paris Saint-Germain took another stride towards the Ligue 1 crown, beating Angers 3-0 to open up a six-point advantage over Lens at the top of the table. Lee Kang-in and Senny Mayulu struck first-half goals in Angers, with Lucas Beraldo finding a third shortly after half-time to keep PSG on course for a 12th French title in 14 years.

It was a largely ideal afternoon for PSG ahead of Tuesday’s Champions League semi-final first leg at home to Bayern Munich, although Achraf Hakimi is an injury concern after he came off at half-time. PSG also finished the game with 10 men as Goncalo Ramos saw red on 74 minutes after receiving a second yellow card.

Lyon held off lowly Auxerre 3-2 in Ligue 1 earlier in the day to keep their Champions League ambitions on track. A Roman Yaremchuk double, either side of a Corentin Tolisso goal, was enough to move the hosts to 57 points and open up a provisional three point gap to fourth-placed Lille.