Frankfurt coach Armin Veh was later ordered to the stands for protesting a penalty decision that didn't go his way.
"Someone has to be shot in the penalty area for us to get a penalty," Veh said.
TV replays showed Pirmin Schwegler went down under what seemed light contact from Hannover defender Hiroki Sakai.
Veh's mood worsened when Vaclav Kadlec then bundled Prib over at the other end, leading to the free kick that Huszti brilliantly converted.
"It's clear that we couldn't put the opponent under pressure. But we also didn't allow much," said Veh, whose side is now winless in nine games.
Hannover captain Steve Cherundolo came on in injury time to make his long-awaited comeback from injury to a rousing reception from fans.
The 34-year-old American defender played five games in April and May after left knee surgery in February, but underwent another knee operation in August.
Later Sunday, Raffael's second-half goal was enough for fourth-place Borussia Moenchengladbach to beat Freiburg 1-0 and stretch its winning run to five games.
The Brazilian scored with a tap-in in the 62nd, when Oscar Wendt crossed for him to finish after Patrick Herrmann sprung the offside trap to send him through.
Herrmann had the best chance before that, displaying good technique to shoot on the volley in the 27th, only to be denied by Oliver Baumann, who pushed the ball onto the crossbar.
Sebastian Freis had Freiburg's best chance in the 58th but mishit the ball with only the goalkeeper to beat.
"It's hard to score goals against this side. They've improved a lot in the last three, four weeks," said Moenchengladbach coach Lucien Favre after his side's seventh consecutive win at home.
Moenchengladbach survived a late onslaught from the visiting side, which remains in the relegation playoff place level on points with Frankfurt after its seventh defeat of the season.
