Lewandowski struck with Bayern's fastest goal of the season thus far on six minutes, following Rafinha's superb long pass, and Robben added a second with a fine individual effort seven minutes later.
A dominant first-half performance brought a third goal when Lewandowski was picked out by another excellent ball from distance, this time from Xherdan Shaqiri, and poked home.
Robben then wrapped up a routine triumph 11 minutes from time with a well-taken finish.
The result sees Pep Guardiola's side keep their place at the top of the Bundesliga and will be seen as the ideal answer to recent critics.
Despite coming into the game two points clear of Borussia Monchengladbach at the summit of the table, Guardiola's men had faced criticism for not showing the attacking ruthlessness they displayed last season.
However, they were given an ideal start when Rafinha picked out Lewandowski's superb run through the heart of the defence with a fantastic long ball, allowing the Polish striker to beat the offside trap and apply a calm finish.
It was a deserved reward for the hosts, who showed plenty of positive intent during a dominant first-half performance, with Robben typically lively.
The Dutchman grabbed Bayern's second on 13 minutes, taking advantage of a gaping hole in the middle of the Hannover defence to race into the area and slot home.
Robben nearly doubled his tally three minutes later, cutting inside from the left before curling just wide of the post, much to the relief of Hannover goalkeeper Ron-Robert Zieler.
Zieler had to be alert to keep his side falling further behind after 20 minutes, back-pedalling to tip Xabi Alonso's audacious lob from the halfway line over the bar.
Bayern continued to press, with Robben firing over 10 minutes before half-time following a great lay-off from Lewandowski, who should then have headed a third for the hosts.
The former Dortmund star made amends for that miss seven minutes before the break, latching on to Shaqiri's wonderful pass from inside his own half and prodding home an effort off the left-hand post.
Hannover very nearly pulled one back before the break, when Artur Sobiech beat the offside trap and burst into the box, only to be denied by a smart save from Manuel Neuer.
Bayern took their foot off the gas a little after half-time, although Robben and Lewandowksi remained a threat.
The two players combined well on the hour mark, with Lewandowski heading over Robben's whipped cross from the right, and the former saw another effort deflect over the bar six minutes later.
Robben's jinking runs continued to cause problems and he was denied by Marcelo's block on 70 minutes.
Despite being shut out on that occasion, it was Robben who rounded off a seventh straight win over Tayfun Korkut's side, picking up a deflected pass from substitute Claudio Pizarro and firing past Zieler with a clinical finish at the near post.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.