DFL Supercup: Eintracht Frankfurt 0-5 Bayern Munich
Kovac masterminded a Frankfurt win in the DFB-Pokal final over Bayern in May, but the Bavarian side inflicted its revenge at the Commerzbank-Arena on Monday (AEST).
Lewandowski starred, netting the first official goal of the Kovac era in the 21st minute, before taking advantage of poor goalkeeping from Frederik Ronnow to double his tally.
Frankfurt showed brief signs of recovery before the interval, but new boss Adi Hutter was left to rue more defensive errors when Lewandowski and Kinglsey Coman put Bayern out of sight before Thiago completed the rout.
Bayern did not take long to click into gear, Lewandowski heading home from Joshua Kimmich's cross.
Lewandowski had his second five minutes later, nodding in an Arjen Robben corner after Frankfurt new boy Ronnow was caught in no man's land.
Any hopes of a Frankfurt comeback were ended in the 54th minute, Lewandowski regaining possession high upfield before coolly slotting in his third.
Ronnow's debut was made worse just after the hour, as he palmed David Alaba's cross into the path of Coman, who made no mistake.
Coman turned provider late on as Bayern ran riot, Thiago getting in on the act with a confident finish to cap a brilliant start for Kovac.
Frankfurt's task to retain its DFB-Pokal crown starts with a trip to minnow SSV Ulm 1846, while Bayern will face SV Drochtersen/Assel before starting its Bundesliga campaign against Hoffenheim.