Poland international Lewandowski, yet to deliver the goal rush that was expected after he joined from Borussia Dortmund this season, has not been an automatic starter.
Coach Pep Guardiola publicly backed the striker on Friday, saying he did not always play because of different systems.
Lewandowski, a late substitute in the goalless draw at Shakhtar Donetsk in the Champions League this week, opened the scoring in the 24th minute by pouncing on a superb flick from Robben.
Then, in true centre forward fashion, he tapped in a Franck Ribery cut-back 13 minutes later. Paderborn’s fate was sealed when Florian Hartherz was sent off after 62 minutes and Robben converted the resulting penalty.
Ribery and Mitchell Weiser were also on target before Robben notched his 16th league goal of the campaign to equal his best tally for the club and climb to the top of the Bundesliga scorers’ list.
“We were very serious today and allowed hardly any chances,” Guardiola told reporters. “It was at times hard to play against a five-man defence.”
Bayern, who have amassed 14 goals in their last two league games, have 55 points from 22 matches.
Elsewhere, Werder Bremen stunned fourth-placed Schalke 04 as a last-minute equaliser from Sebastian Proedl snatched a 1-1 draw.
Schalke, beaten 2-0 in the Champions League by Real Madrid in midweek, took the lead through Max Meyer before Proedl levelled after meeting a free kick with a powerful header.
Marwin Hitz became the third goalkeeper in Bundesliga history to score from open play as he produced a stoppage-time equaliser to secure Augsburg a 2-2 home draw with Bayer Leverkusen.
Leverkusen, in sixth spot on 33 points, twice let the lead slip in their last game before they meet Atletico Madrid in the Champions League last 16 next week.
New Mainz 05 coach Martin Schmidt enjoyed a winning Bundesliga debut as his team eased past Eintracht Frankfurt 3-1 to climb up to 11th on 25 points.
Hanover 96 drew 1-1 at Cologne to remain 10th but will be without Joao Pereira next week against Stuttgart after he was sent off in stoppage time.
Second-placed VfL Wolfsburg, on 44 points, are in action on Sunday at home to Hertha Berlin.
(Editing by Ed Osmond)