The Bavarians made a slow and sluggish start before the Poland forward put them in front with a 37th-minute penalty after Thomas Mueller was brought down.
Hamburg remained disciplined at the back and got their reward eight minutes into the second half when Xabi Alonso put an Aaron Hunt free kick through his own net.
Lewandowski restored Bayern's lead in the 61st minute, deflecting Mueller's shot and wrong-footing keeper Rene Adler to take his Bundesliga goal tally for the season to 17, one behind Borussia Dortmund's Pierre-Emerick Aubameyang.
David Alaba then hit the post with a superb free kick as Pep Guardiola's Bayern carved out more scoring chances late on.
"We needed a bit of time after the one-month break and today it was all about the three points," Lewandowski told reporters.
"We will improve. It is a long season and we cannot (always) be in top form."
There was bad news for the visitors when central defender Jerome Boateng went off in the 56th minute with a suspected adductor muscle injury.
Spaniard Guardiola, who leaves at the end of the season and has said he will be joining an English Premier League club, is chasing his third straight domestic title while the Bavarians are on track for a record fourth consecutive Bundesliga crown.
Bayern have 49 points from 18 games. Dortmund, in second place on 38, travel to Borussia Moenchengladbach on Saturday when third-placed Hertha Berlin, on 32, host Augsburg.
(Reporting by Karolos Grohmann; Editing by Tony Jimenez)
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