WATCH the Bundesliga LIVE on beIN SPORTS | Sign up to take advantage of our 7-day FREE TRIAL here | AU | NZ

The victory marked a successful debut for new coach Kasper Hjulmand, who took over this week after the sacking of Erik ten Hag after Leverkusen failed to win either of its first two league matches.

The hosts looked sharper under the Dane, quickly taking control and leaving Eintracht, which had won its previous two league matches this season, to play a supporting role in the first half. But Leverkusen had two players sent off in the second half.

The result ended Frankfurt's unbeaten run of eight matches that stretched back to last season.

Leverkusen, which will travel to FC Copenhagen for its UEFA Champions League opener next week, opened its account with Spain international Grimaldo's stunning 25-metre free-kick into the top corner.

Nathan Tella and Patrik Schick each came close before the latter bagged a second goal with a stoppage-time penalty, awarded for a foul on the former.

The visitors, who host Galatasaray next week in the UEFA Champions League, pulled a goal back seven minutes after the restart with Can Uzun's volley and in the 59th Leverkusen saw captain Robert Andrich dismissed for a second booking.

Tella should have scored again in the 84th but keeper Michael Zetterer blocked his close-range shot.

The hosts were then left with nine players after Ezequiel Fernandez got his marching orders with a second yellow card in a bad-tempered finale before Grimaldo settled nerves with another superbly taken free-kick in stoppage-time for his second goal of the evening.

Despite the tumultuous nature of his first match in charge, Hjulmand walked away from BayArena in high spirits.

"What a match. A lot happened, but we got the three points, and I am very happy," Hjulmand said.

"I said congratulations – also that I think we did not allow many chances, that we had a lot of energy, and that we worked a lot defensively.

"We can definitely improve, of course, but three points are very important for us."

"It was very nice in the stadium, a lot of energy – as I said on the defensive side, our high pressing was good in the first half," Hjulmand added.

"I think we were very, very compact with the back line; we did not allow much, only two shots. We created chances and were strong when we needed to press."

When asked how he handled the situation relating to the two red cards, he said: "I do not want to criticise too much – I think that there was one major misunderstanding.

"[Regarding Ezequiel Fernandez's motion to referee Deniz Aytekin], I think that the official saw a hand movement, and it was a complete misunderstanding. But apart from that, I have not seen it a second time.

"I just want to enjoy the win, and then we will see."