A goal by 18-year-old midfielder Aymen Barkok and two from Sweden striker Branimir Hrgota sealed Eintracht's win.
There was a minute's silence, followed by loud applause, before kick-off at each of the four grounds to pay tribute to the victims of Monday's terror attack at a Berlin Christmas market.
In Frankfurt, a goal by 18-year-old midfielder Aymen Barkok and two from Sweden striker Branimir Hrgota sealed Eintracht's win.
"I'm happy -- with the result and the way the season has gone," said Frankfurt coach Niko Kovac.
"Mainz were a constant threat and we have to thank (goalkeeper) Lukas Hradecky.
"It was easier after the Mainz red card."
Hrgota gave the hosts an early lead following a dream 50-yard pass from centre-back David Abraham.
Mainz had Jhon Cordoba sent off on 55 minutes for stamping on Abraham's foot after a tackle.
Frankfurt capped the win when Barkok came off the bench to net before Hrgota added the third.
Borussia Dortmund, who were missing suspended Germany winger Marco Reus, climbed one place to fourth following a 1-1 draw with Augsburg.
It was the second straight win for caretaker boss Manuel Baum as Augsburg look for a new coach.
The visitors took a shock lead at Dortmund's Signal Iduna Park when centre-back Martin Hinteregger sprinted through five Borussia defenders before Ji Dong-Won was put into space.
The South Korea striker had his first shot parried before firing the rebound into an empty net on 33 minutes.
Dortmund equalised after the break when Japan's Shinji Kagawa broke through the middle and set up Ousmane Dembele, who held off a defender and rolled his shot home.
Before kick-off, Dortmund announced they had extended the contract of Germany midfielder Julian Weigl until 2021.
"We allowed Augsburg too many chances," admitted Weigl.
Borussia Moechengladbach coach Andre Schubert is a prime candidate to become the seventh Bundesliga coach sacked since September after their 2-1 home defeat to Wolfsburg.
Daniel Caligiuri put Wolves ahead with a shot into the top corner on three minutes.
Gladbach drew level when Thorgan Hazard netted on 52 minutes.
Wolfsburg regained the lead as Germany striker Mario Gomez rounded goalkeeper Yann Sommer and slotted into an empty net on 57 minutes.
Gladbach's director of sport Max Eberl had implied the team had to win their last three matches before Christmas for Schubert's job to be safe.
A scrappy 1-0 win over Mainz a fortnight ago, Saturday's 1-0 defeat to Augsburg and the loss to Wolves is a poor return with the team four points from the relegation places.
"I know that a response is required, but I will not announce a decision now -- give us one night," Eberl told Sky.
"The game was governed by an incredible amount of nervousness. It was a pity, the players tried hard."
Despite picking up his second straight win, Wolfsburg coach Valerien Ismael could also lose his job in the winter break.
German media reports suggest Huddersfield Town's German coach David Wagner has been approached to take over.
Schalke are down to 11th after their 2-1 defeat at relegation-threatened Hamburg as Nicolai Mueller and Bobby Wood scored second-half goals for the hosts.
Hamburg's Johan Djourou had a second-half penalty saved while Donis Avdijaj scored Schalke's consolation in the final minute.
The key clash of the midweek round is Wednesday's showdown when leaders Bayern Munich host second-placed RB Leipzig at the Allianz Arena with a sell-out crowd of 75,000 expected.