The Poland international's first-half double proved decisive as Pep Guardiola's charges won their fourth straight Bundesliga crown at the Audi Sportpark on Saturday.
Bayern Munich were crowned Bundesliga champions for a fourth season in a row after they beat Ingolstadt 2-1 at the Audi Sportpark on Saturday.
The Bavarians put their midweek Champions League misery behind them as they secured their 27th league win this season, though Borussia Dortmund's surprise 1-0 loss to Frankfurt meant Bayern only needed a point to get their hands on the title.
Marvin Matip fouled Franck Ribery inside the Ingolstadt penalty area and Robert Lewandowski made no mistake from the spot to get Bayern up and running after 15 minutes.
Lewandowski got his name on the scoresheet again soon after but Bayern's lead was halved when Moritz Hartmann was brought down by Xabi Alonso, before converting a penalty of his own three minutes before the interval.
However an impressive performance from Ingolstadt failed to result in an equaliser as Bayern were able to hold on for all three points.
Bayern were made to wait for the title after being held to a 1-1 draw by Borussia Monchengladbach last weekend and came out the traps fast against Ingolstadt.
Bayern needed just 15 minutes to open the scoring through Lewandowski. Matip brought down Ribery inside the Ingolstadt area, leaving referee Florian Meyer little choice but to point to the spot, and the Poland international coolly slotted home for his 40th goal of the season in all competitions.
Douglas Costa should have made it two halfway through the first half after being sent clean through by Lewandowski, but the Brazilian hesitated too long in front of goalkeeper Ramazan Ozcan, allowing Benjamin Hubner to rush back and make a last-ditch tackle.
Ingolstadt caused Bayern plenty of problems on the break, though, and Hartmann should have levelled the scores after a good combination with Dario Lezcano, only to see his shot from 10 yards go inches wide.
The hosts were made to pay for Hartmann’s miss in the 32nd minute and it was Lewandowski who again found the net. Alonso picked the striker out with a sublime ball in behind the Ingolstadt defence and he beat Ozcan with a calm finish into the far corner.
Lewandowski could have had a first-half hat-trick after beating the offside trap and rounding Ozcan, but Hubner once more came to the rescue for the hosts with a goal-line block.
Ingolstadt never gave up and Hartmann deservedly pulled one back in the 42nd minute, converting a penalty after he was fouled by Alonso.
David Alaba and Costa fired wide from dangerous positions early in the second half as Bayern looked to finish the game off, while Thomas Muller was denied by Ozcan after a brilliant throughball from Thiago Alcantara.
Ingolstadt, though, continued to charge forward in search of an equaliser whenever possible and Hartmann was unfortunate not to net his second goal of the afternoon when he fired just wide in the 70th minute.
But Bayern held on to their narrow lead to lift their first major trophy of 2015-16, in what will be Pep Guardiola's final campaign in charge of the club.
