Vaclav Kadlec fired the Bundesliga side in front early on and, after Tal Ben Haim was given his marching orders, Alexander Meier made sure of the points which lift Eintracht five points clear of their opponents.
Maccabi remain in second spot but now have Bordeaux breathing down their necks after the French club's victory over Apoel Nicosia.
The warning signs were there from the early stages when visiting goalkeeper Juan Pablo had to tip Meier's header over the crossbar after just four minutes.
Ben Haim then tested Eintracht keeper Kevin Trapp with his left-footed strike before Juan Pablo made another good stop to deny Tranquillo Barnetta in a frantic opening spell.
But the home side soon asserted their authority with the opening goal after 12 minutes. A header from Meier came back off the crossbar but fell kindly for Kadlec, who had an easy tap-in from six yards.
Barnetta tried his luck again after 25 minutes as Eintracht looked to build on their lead but could only push his shot past the right post.
However, the home side were given a helping hand with the dismissal of Ben Haim after 34 minutes - the striker picking up two bookings in the space of five minutes.
With their man advantage, Eintracht quickly set about turning up the heat on their opponents and Juan Pablo made saves from Barnetta, Meier and Marco Russ to keep the Israeli side in it at half-time.
It took just eight minutes of the second half for the German hosts to find the target again, with Barnetta's in-swinging corner headed in by Meier.
And there was no way back for Maccabi, who have their goalkeeper to thank for keeping the scorelines respectable with Kadlec, Srdjan Lakic and Bastian Oczipka all kept at bay by some brilliant work from Juan Pablo.