The defending Bundesliga champions suffered their first draw of the season last time out and got off to a horrible start against St Pauli when Andreas Hountondji got on the end of a Mathias Lage throughball to put the visitors ahead in the sixth minute.
The Bavarians dominated large swathes of the game with 80% of the possession but had to wait until a minute before half-time before they found an equaliser.
Diaz looked to have been fouled in the box but kept his wits about him to poke the ball to Raphael Guerreiro, who finished with power to level the scores.
St Pauli clung on for dear life in the second half and nearly claimed a draw but a late flurry from Bayern stole the points late on.
Diaz latched on to a cross from Joshua Kimmich to head the hosts into the lead three minutes into stoppage time to put them 2-1 ahead before Nicolas Jackson stole a third three minutes later to put a bit of gloss on the scoreline.
Elsewhere in the Bundesliga on Saturday, TSG Hoffenheim hammered Augsburg 3-0 with Bazoumana Toure (16') and Wouter Burger (26') getting on the scoresheet before a Cedric Zesiger own goal (45') rounded out the scoring.
Borussia Dortmund claimed an impressive 2-1 win away from home against Bayer Leverkusen with Aaron Anselmino (41') and Karim Adeyemi (65') grabbing goals for the visitors before Christian Kofane (83') bagged a late consolation.
Heidenheim struck late to steal an unexpected 2-1 victory over Union Berlin at An der alten Forsterei.
Rani Khedira put the home side ahead in the 43rd minute and they maintained that lead all the way to the 90th when Stefan Schimmer levelled the scores.
Jan Schoppner then grabbed a dramatic winner five minutes later to secure an unlikely win for the visitors.
Marco Friedl (22') and Said El Mala (90+1) exchanged strikes as Werder Bremen and FC Koln drew 1-1 at Weserstadion.
VfB Stuttgart have been dealt another major setback after defender Dan-Axel Zagadou suffered a fresh muscle injury during training ahead of their Europa League match against Go Ahead Eagles tonight at De Adelaarshorst stadium.
Bayern Munich's board have moved to shut down any doubts around Vincent Kompany's future, with Max Eberl insisting that the Belgian is already proving himself as a long-term leader at the club.
Harry Kane's future moved back into the spotlight after Bayern Munich fell 3-1 to Arsenal in the Champions League league phase on Wednesday night, with the England captain unable to add to his impressive scoring record.
Vincent Kompany said Bayern Munich are fully focused on producing a sharp response when they meet struggling St. Pauli in the Bundesliga on Saturday, just three days after their 3-1 Champions League defeat to Arsenal.
