Alex Garcia got the home side off to the best possible start, giving them the lead with a shot that was deflected off Jonathan Tah to wrong-foot Sven Ulreich.
Tah thought he had grabbed an equaliser around the half-hour mark but it was disallowed for offside.
The Bavarians' task was made more complicated three minutes before the break when Nicholas Jackson was shown a straight red card for a late tackle on Martin Terrier.
Fit again Harry Kane was introduced off the bench in the 61st minute and had the ball in the back of the net within two minutes of being on the pitch but the strike was ruled out for offside.
Diaz finally found a leveller for Bayern around 70 minutes into the game after getting on the end of a Michael Olise pass before sliding a neat finish past Janis Blaswich.
However, with six minutes left on the clock, Diaz was shown a second yellow card for simulation and earned an early shower.
Leverkusen made the most of their numerical advantage and pushed for a late winner, with Jonas Hofmann lobbing the ball over Ulreich in stoppage time only for the goal to be ruled out for offside.
Christian Kofane also thought he had scored a late winner but Ibrahim Maza fouled Ulreigh in the lead-up and both teams had to settle for a point.
Elsewhere in the Bundesliga, Borussia Dortmund made the most of Bayern dropping points with a 2-0 win over Augsburg at Signal Iduna Park thanks to goals from Karim Adeyemi (13') and Luca Reggiani (59').
Eintract Frankfurt beat Heidenheim 1-0 at Deutsche Bank Park despite being reduced to 10 men after Robin Koch being sent off for receiving two yellow cards, with Arnaud Kalimuendo scoring the winner in the 53rd minute.
Hoffenheim and Wolfsburg drew 1-1 at PreZero Arena with Konstantinos Koulierakis putting the visitors ahead in the 64th minute before Grischa Promel rescued a point for the hosts in the 83rd minute.
HSV and FC Koln also shared the points at Volksparkstadion with Fabio Vieira (39') and Said El Mala (45') exchanging goals for the third 1-1 stalemate of the day.
Borussia Monchengladbach cruised to a comfortable 2-0 win over St Pauli at Borussia Park with Kevin Stoger (37') and Franck Honorat (62') getting on the scoresheet.
Niko Kovac has said Borussia Dortmund were determined to build momentum when they host FC Augsburg in the Bundesliga on Saturday, with the coach also providing key updates on several players ahead of the match.
Bayer Leverkusen return to Bundesliga action on Saturday as hosts to leaders Bayern Munich, still grappling with inconsistency that threatens their top-four ambitions.
Sebastian Hoeness has admitted his side “briefly lost composure” during a costly spell as VfB Stuttgart slipped to a 2-1 defeat against FC Porto in the first leg of their UEFA Europa League round of 16 clash on Thursday night.
Kasper Hjulmand was left furious after a controversial late penalty allowed Arsenal to snatch a 1-1 draw against Bayer Leverkusen in the first leg of their UEFA Champions League round-of-16 tie on Wednesday night.
