Borussia Dortmund's 4-2 defeat to Hannover earlier on Saturday meant either of these teams could have gone to the summit, but there only ever looked like being one winner after Orban's 13th-minute dismissal as Jupp Heynckes' men cruised.
It quickly became apparent that Leipzig were in for a long day in Munich, Orban sent off for a professional foul on Arjen Robben with the help of VAR and James Rodriguez – who has struggled so far at Bayern – opening the scoring after a fine move in the 19th minute.
Lewandowski essentially wrapped things up with a cool finish before half-time, though he then had to be withdrawn with what appeared to be a hamstring problem, making him a doubt for Tuesday's Champions League trip to Celtic.
Without their talismanic striker, Bayern were a little less potent in attack and that resulted in a lack of clear-cut opportunities in a second half which had few highlights.
But their control on proceedings showed no sign of dissipating, as Heynckes' side followed up their DFB-Pokal penalty shoot-out win over Leipzig in midweek by playing some eye-catching football towards the end of a straightforward triumph.
Bayern made a purposeful start and went close to breaking the deadlock after just two minutes, Javi Martinez heading agonisingly wide after David Alaba's 20-yard drive was deflected wide.
The Spaniard was proving a real nuisance at set-pieces and he nodded just off target again shortly after.
Bayern then received a massive boost as Orban was dismissed for barging Robben over when through on goal.
And Bayern had a deserved lead a few moments later – James tucking a first-time effort just inside the right-hand post after Robben produced a pinpoint low cross from the flank at the end of a charging run.
The chances continued to flow for Bayern, with James seeing a dipping volley deflected just over, before Peter Gulacsi made a strong save to keep a Lewandowski header out.
But the Pole was not to be denied just before the break as he raced on to Martinez's pass and coolly found the bottom-right corner, though he was withdrawn with a suspected hamstring problem before the half was out.
Bayern were not quite as free-flowing in attack upon the restart, but they did create a couple of half-chances in their search for a third goal, Alaba lashing into the side-netting before Robben shot straight at Gulasci.
The hosts seemed to become more intent on retaining possession and tiring out their visitors, who almost scored an own goal through Lukas Klostermann when Joshua Kimmich flashed a ball across the face of goal just after the hour mark.
Martinez attempted to add a spectacular third 10 minutes from the end when he blasted just wide of the top-right corner from 30 yards.
That miss mattered little, however, as the home side strolled to a fifth straight victory under Heynckes.
