Having been publicly criticised by Bayern CEO Karl-Heinz Rummenigge following his comments regarding the Bundesliga champions' transfer policy, Lewandowski wasted no time in making an impact when he drew a clumsy foul from Sven Kums 11 minutes in.
Though the initial contact may well have been outside of the area, a penalty was awarded - and Kums was given his marching orders - with Lewandowski making no mistake from 12 yards.
Bayern came into Tuesday's clash on the back of their first defeat of the season, which came at the hands of Hoffenheim, and Die Rotten were far from at their best once more, with the visitors squandering two excellent opportunities to restore parity either side of half time.
But, Bayern finally clicked into gear just after the hour, Thiago Alcantara tucking home from Joshua Kimmich's pinpoint cross.
An argument between Lewandowski and Arjen Robben and the touchline antics of Franck Ribery threatened to overshadow Bayern's return to form, but Kimmich's late effort ensured a routine victory ended on a high note.
James Rodriguez should have marked his full debut with a goal inside 10 minutes, but could only direct a tame header straight at Matz Sels after meeting Ribery's inch-perfect cross.
However, Bayern did not have to wait long to take the lead.
Having latched onto a ball over the top of Anderlecht's defence, Lewandowski raced into the area, drawing a desperate foul from Kums who - as the last man - the referee had little choice but to send off.
Lewandowski duly converted from the spot, sending Sels the wrong way with a composed finish into the bottom-left corner.
Despite their numerical advantage, a close-range Lewandowski header was the closest Bayern went to extending their lead, and Anderlecht should have drawn level prior to the interval.
Leander Dendoncker got in behind Bayern's defence and teed up Nicolae Stanciu but, having slipped at the vital moment, he sliced his effort wide as Anderlecht failed to capitalise on a rare venture forward and beat goalkeeper Manuel Neuer - making his 100th appearance in European competition.
And the hosts' vulnerable defence was opened up once again moments after the restart when Sofiane Hanni's cut-back found Alexandru Chipciu, whose effort rebounded agonisingly off the left-hand upright.
Ancelotti's side responded well, though, and finally had their second in the 65th minute as Thiago prodded in Kimmich's low cross.
Niklas Sule thought he had opened his Champions League account with a terrific header soon after, only for the official to deem the former Hoffenheim man had committed a foul in the build up.
Bayern were back at their rampant best, but issues arose late on when Lewandowski shrugged off Robben's complaints after the Poland striker failed to play in the Dutch winger before, having been substituted, Ribery launched his shirt down onto the bench.
But that petulance from Bayern’s experienced front line was put to one side in stoppage time, youngster Kimmich coolly rounding Sels to add further gloss to the win.