Coach Pep Guardiola claimed he only had 14 fit players available in the run up to Saturday's game and named just four substitutes as a result, but runaway leaders Bayern made light of their injury problems and were led superbly by Lewandowski
The Pole struck first after quarter of an hour, producing a superb touch on the edge of the area with his back to goal before turning to lash home an unstoppable effort.
Mario Gotze crashed a drive against the post just after the hour before Lewandowski doubled his tally with a close-range header to make it 16 goals for the season in the Bundesliga.
Only the woodwork denied Lewandowski a hat-trick late on, with Thomas Muller adding a third with a cool slotted finish.
The result boosts Bayern's bid for a domestic and European treble and leaves them in confident mood ahead of their UEFA Champions League quarter-final first leg with Porto on Wednesday.
Despite their recent injury worries, Bayern dominated possession during the opening exchanges and were rewarded for their early efforts in spectacular fashion after 15 minutes.
A chipped ball from Muller found Lewandowski with his back to goal on the edge of the area before a deft touch allowed the Poland international to turn and fire a vicious volley into the top corner.
The legs of goalkeeper Kevin Trapp prevented Lewandowski from doubling his tally five minutes later and another smart save was enough to keep out the bustling striker's poked finish soon after.
Bayern goalkeeper Pepe Reina, preferred ahead of regular number one Manuel Neuer, was eventually called into action just before the break to deny Sonny Kittel after a rare Eintracht foray forward, but the hosts remained largely untroubled.
The home side had the ball in the net when Muller slotted home moments later, but a second goal was ruled out for offside after much deliberation between referee Markus Schmidt and his assistant.
The hosts continued to attack with purpose after the break, with Gotze rattling the post with a low drive just after the hour.
Eintracht, missing Bundesliga top scorer Alex Meier, still could not fashion any notable opportunities and were inevitably punished after 66 minutes.
A brilliant breakaway move allowed Gotze to get a shot away inside the area that was initially well blocked on the line by Makoto Hasebe, only for Lewandowski to head the rebound into an unguarded net.
Sebastian Rode was introduced late on to face his former club, but Lewandowski remained the star attraction, hitting the post 15 minutes from time.
But Bayern were not to be denied a third, with Muller bursting into the box before slotting past an onrushing Trapp and round off a thoroughly satisfying afternoon for the defending champions.
