Pep Guardiola's men were crowned champions in late March, but have seen their form tail off in recent weeks, with Stuttgart looking all set to further Bayern for much of Saturday's match.
That was until Pizarro fired in a left-footed shot from the edge of the area with the last kick of the game, as Bayern put the seal on their title-winning season before being presented with the trophy afterwards.
The hosts dominated at the Allianz Arena throughout and were almost kept out by Stuttgart, who toiled manfully and regularly dropped 10 men behind the ball in a rigid defensive effort.
Mario Mandzukic failed in his bid to become the Bundesliga's leading scorer ahead of Borussia Dortmund's Robert Lewandowski as he was denied by a combination of good goalkeeping and wayward finishing before limping out of action in the second half.
Pizarro, on as Mandzukic's replacement, was equally wasteful initially, blazing over the crossbar while unmarked in the 75th minute.
Stuttgart, whose safety was assured last week, created little going forward and have now lost 11 consecutive matches to Bayern in all competitions.
Despite the win, Bayern will have concerns over Mandzukic's fitness, while Bastian Schweinsteiger also sustained an injury and both players are now seemingly a doubt for the DFB-Pokal final against Dortmund next weekend.
After a quiet opening to the game, Mandzukic had the first serious effort on goal in the 24th minute.
The Croatian, recalled to the side in place of Mario Gotze, let fly from the corner of the penalty area, but Sven Ulreich was equal to his attempt and tipped the ball around the post.
Four minutes later, Mandzukic and then Schweinsteiger both headed narrowly off target as Bayern began to assert themselves.
The hosts felt they should have had a penalty shortly after the half-hour when Mandzukic's acrobatic volley cannoned off the arm of Gotoku Sakai, but referee Bastian Dankert awarded a corner only.
Bayern began the second half as they had ended the first and were camped in the Stuttgart half, Arjen Robben bringing a flying save out of Ulreich shortly after the hour.
Tempers momentarily flared when Dante brought down Stuttgart substitute Cacau midway through the half, with the referee showing the Brazilian defender a yellow card after passions were calmed.
Mandzukic had hobbled off injured shortly beforehand and Pizarro wasted the clearest opening of the match with when he ballooned over the crossbar after being picked out by David Alaba's cutback with 15 minutes to go.
Robben was denied by Ulreich with five minutes to go before Pizarro struck from 20 yards as Bayern signed off a dominant season with a win in front of their home fans.
