Leverkusen, who had lost momentum under former coach Erik Ten Hag, finally got off the mark with a strong display despite being reduced to nine players.
Spain international Alex Grimaldo stood out, scoring two free kicks, one in each half, and Patrik Schick added a penalty deep in stoppage time when Nathan Tella was fouled.
Frankurt's goal was scored by Can Uzun, but they could not make use of their numerical advantage after Leverkusen saw Robert Andrich and Ezequiel Fernandez both sent off in the second half.
Speaking after the match, Hjulmand said: "What a match. A lot happened this evening, but we got the three points and I am very happy."
He praised the defensive effort, saying, "We did not allow many chances, we had a lot of energy, and we worked a lot defensively. We can definitely improve, of course, but three points are very important for us."
When asked about the red cards, Hjulmand described one of the dismissals, the one involving Fernández, as a misunderstanding: "The official saw a hand movement like this … and it was a complete misunderstanding." He added that beyond that, he just wants to "enjoy the win."
Leverkusen also continue to adjust after a summer of big departures. Florian Wirtz is no longer at the club, he joined Liverpool earlier this summer for a British-record fee.
Luis Diaz has stormed into the Bayern Munich team with a goal in each of his first three Bundesliga games, a feat only previously achieved at the club by Ruggiero Rizzitelli (1996), Luca Toni (2007) and Mario Mandzukic (2012).
Bayern Munich thrashed HSV 5-0 with Harry Kane bagging a brace on a day that saw four red cards shown in fixtures across the Bundesliga.
Bayern Munich have completed the signing of Senegal striker Nicolas Jackson on a season-long loan from Chelsea, with the 24-year-old expressing his happiness at joining a club where he feels wanted.
VfB Stuttgart chief executive Alexander Wehrle has admitted that the club went through lengthy internal discussions before agreeing to sell Nick Woltemade to Newcastle United during the transfer window.
