Former Bayern player Kovac was announced as Jupp Heynckes' successor in April, having impressed at Frankfurt in the past two seasons.
However, in a dress rehearsal for the DFB-Pokal final, it was Heynckes, despite having made eight changes to Bayern's starting XI ahead of the Champions League clash with Real Madrid, who triumphed thanks to goals from Niklas Dorsch, Sandro Wagner, Rafinha and Niklas Sule.
Dorsch marked his Bayern debut in style on 43 minutes, although it could have been different for Frankfurt, with both Mijat Gacinovic and Luka Jovic having passed up gilt-edged chances.
Wagner's well-taken goal looked to have put the game beyond all doubt with 14 minutes remaining, only for Sebastien Haller to set up a grandstand finish.
Ultimately though, Frankfurt's spirited fightback came to nothing, substitutes Rafinha and Sule making Bayern's victory emphatic late on.
Kovac could have got off to the ideal start against his future employers inside the opening 10 minutes, only for Jovic to fire a tame effort at Sven Ulreich following a well-crafted Frankfurt counter-attack.
One of three Bayern debutants, Franck Evina was the first to go close for the hosts with a long-range effort that curled wide, before Wagner drew a fine save from Lukas Hradecky.
Evina continued to impress, but Frankfurt should have taken the lead prior to half-time.
First, Gacinovic failed to hit the target with a first-time strike from the edge of the box before, moments later, Jovic fired straight at Ulreich, having got one-on-one with Bayern's goalkeeper.
Bayern were quick to make Frankfurt pay - Wagner leaving the visitors' defence in his wake to tee up Dorsch, who made no mistake with a neat finish.
Despite Bayern's lead, Frankfurt continued to threaten - Jovic just failing to apply the finishing touch to Danny da Costa's low cross.
Wagner should have doubled Bayern's tally just after the hour, but the striker could not turn Evina's cross in.
The former Hoffenheim man made amends when he slotted home after good work from Sebastian Rudy.
Haller bundled in Da Costa's cross from close range to make things interesting with 12 minutes remaining, but it was Bayern who would have the final say.
Dreadful defending from Frankfurt enabled Rafinha to race clear, and the full-back duly slotted in his first Bundesliga goal since 2016.
Fellow substitute Sule, playing in a holding midfield role, would add further gloss to the victory in the final minute - driving through Frankfurt's lines before drilling in a low finish to tee Bayern up perfectly for Tuesday's trip to Madrid.
Key Opta Facts:
- Bayern’s starting XI had an average age of 24 years and 35 days. It was their youngest starting XI in the Bundesliga since 1971 and almost six years younger than the starting XI against Real Madrid during the week (29 years, 318 days).
- Niklas Dorsch scored in his first competitive match for Bayern with his first shot.
- For the first time since February/March 2015, Bayern have scored at least three goals in five Bundesliga matches in a row.