Dortmund beat Mainz to keep Champions League hopes alive
Champions League finalists last season, Dortmund had lost four of their past six games to sink to 12th before the match.
Dortmund were without injured striker Serhou Guirassy but Beier filled the void as he gave the hosts the lead after 32 minutes, finishing off a goal he initiated.
The 22-year-old Germany forward gathered the ball in midfield, shed a defender and found Julian Brandt who whipped in a cross and Beier threaded the ball to Karim Adeyemi, who returned the favour, giving him a simple tap-in.
Emre Can doubled Dortmund's lead just four minutes later, heading in a Nico Schlotterbeck corner.
Schlotterbeck supplied Dortmund's third as well in the 72nd minute, floating in a superb ball which allowed Beier to head home, before Mainz pulled one back through Paul Nebel.
Dortmund manager Niko Kovac said there was "nothing more beautiful than winning in football", but added his side's work was only just getting started.
"We won today but with seven games left, we've got plenty more to do," Kovac told DAZN.
The win was Dortmund's first victory over Mainz in four attempts, including the infamous 2-2 draw against the same opponents on the final day of the 2022-23 season which cost them the title.
Dortmund now sit 10th, four points behind the European places and seven points back from Mainz, who are in fourth.
Despite the loss, Mainz are two points clear of fifth-placed Borussia Moenchengladbach and are in with an excellent chance of a first-ever Champions League appearance.
Union Berlin won 2-1 at Freiburg, denting their opponents' Champions League hopes while taking a major step towards maintaining their own status as a top-flight team next season.
Freiburg took the lead with 29 minutes played when Lucas Hoeler hammered in a Vincenzo Grifo cross.
The visitors hit back just one minute later, captain Rani Khedira firing in following an Andrej Ilic assist.
Ilic then got on the scoresheet three minutes into the second half, heading a Tim Skarke cross into the top corner.
The loss, just Freiburg's third home defeat of the season, leaves them in seventh, three points off the top four. Freiburg have also never played in the Champions League.
The win took Union, who needed a final-day victory last season at home against Freiburg to avoid dropping into the second division, to 30 points, eight clear of the relegation playoff spot.
Union's recent form looks to have lifted the club out of the relegation mire.
In the past three weeks, Union have beaten top-four hopefuls Eintracht Frankfurt and Freiburg, while holding league leaders Bayern Munich to a draw at home.