Their second straight league win after four consecutive defeats lifted Hanover to 12th place with 35 points, behind Frankfurt on goal difference, and put eight points between them and the relegation playoff spot with three games left.
Hanover got off to a flying start with Leon Andreasen charging through the Frankfurt defence to head in the opener after two minutes following good work from Christian Pander, but Martin Lanig drew the hosts level in the 13th.
However, Hanover attacked at every possible opportunity and struck twice more in nine minutes with Lars Stindl heading in a Pander free kick in the 20th and Ivorian forward Didier Ya Konan slotting home to give them a two-goal cushion at halftime.
Eintracht, who could have guaranteed their safety with a victory, started the second half poorly as Hanover's Andreasen and substitute Szabolcs Huszti hit the woodwork.
Alex Meier cut the deficit against the run of play when he headed in from seven metres but that was Eintracht's last effort while Hanover missed more chances in the final minutes.
On Saturday Hamburg SV, the only club to have played every season in the Bundesliga since its creation in 1963 but currently stuck in the relegation playoff spot, host fifth-placed VfL Wolfsburg, who are chasing a Champions League spot.
Borussia Dortmund, in second place three points clear of third-placed Schalke 04, host Mainz 05.
- Sports & Recreation
- Leon Andreasen
- Christian Pander
- Martin Lanig