Eintracht director of football Fredi Bobic slammed Bayern for the timing of their approach for Kovac as the race for the top four heats up, and that will likely be the focus again as Leverkusen ultimately ran out comfortable winners.
Julian Brandt gave Leverkusen a 20th-minute lead, heading in his eighth Bundesliga goal of the season.
Mexico midfielder Marco Fabian levelled soon after, though, rounding off a well-worked move with a smart finish.
It remained a tight affair until Volland put Leverkusen ahead again in the 71st minute – breaking the offside trap and coolly beating Lukas Hradecky in the Eintracht goal.
The forward then doubled his tally soon after, knocking in from close range to leave Kovac looking deflated.
And Volland completed his treble late on, tapping in an easy finish to ensure fourth-placed Leverkusen opened up a five-point gap ahead of Eintracht and Hoffenheim.