Modeste, under massive criticism after having scored just once in the league following his arrival this season to replace ailing Sebastien Haller, headed in at the far post with the last touch of the game after also setting up their first goal, to rescue a point for his team and keep Bayern off top spot.
Leon Goretzka had fired the visitors in front in the 33rd minute before Leroy Sane added another in the 53rd in the high-intensity encounter in front of a sold-out 81,000 crowd at the Signal Iduna Park in Dortmund.
Youssoufa Moukoko cut the deficit in the 74th minute to become the youngest scorer in the history of Der Klassiker at 17-years-old as Bayern ended the game with 10 men after Kingsley Coman was sent off in the 90th minute with a second booking.
The Bavarians, who face Viktoria Plzen in the Champions League on Wednesday, are on 16 points as many as Dortmund, with Union Berlin and Freiburg, both on 17, in action on Sunday.
Former Liverpool midfielder Xabi Alonso made a winning start in his first game as Bayer Leverkusen manager as Moussa Diaby scored once and set up two more goals for Jeremie Frimpong in a 4-0 demolition of visiting Schalke.
Diaby, who netted 13 times in the previous campaign but had yet to score this season, thundered in a shot from 22 metres in the 38th minute before setting up Frimpong to drill in from a tight angle three minutes later.
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The pair combined again eight minutes after the restart with Diaby, who was linked with a move to Newcastle in the summer, again the provider and Dutch midfielder Frimpong slotting in from close range for his fourth goal of the season.
Paulinho completed the rout with a well-timed run in the 90th to give Alonso, the former Spain international who replaced Gerardo Seoane on the bench earlier this week, a dream start.
Their second league win of the campaign lifted Leverkusen, who host Porto in the Champions League on Wednesday, off the bottom spots and into 14th on eight points. Promoted Schalke dropped to 16th on six.
AC Milan secured a 2-0 win over struggling rivals Juventus with goals from England defender Fikayo Tomori and midfielder Brahim Diaz in a spirited Serie A clash at the San Siro.
Defending champions Milan provisionally moved up two places to third in the standings on 20 points, level with leaders Napoli and second-placed Atalanta who both have a game in hand.
Juventus, who appeared to have turned a corner after beating Bologna 3-0 at home last weekend, following that up with a 3-1 victory against Maccabi Haifa in the Champions League in midweek, remain eighth on 13 points.
Milan were determined to make up for Wednesday's 3-0 defeat to Chelsea in the Champions League and they made it 1-0 just before the break through Tomori who followed up a shot by Olivier Giroud and rifled the ball into the roof of the net.
Diaz then doubled Milan's lead one minute later when he took advantage of Dusan Vlahovic's mistake and raced towards Juve's goal, finishing off a solo effort with a brilliant strike.
Juve's away form continues to trouble coach Massimiliano Allegri, whose side last won on the road in late April.
They have only picked up two points in four Serie A away matches this season and face a testing trip to Maccabi Haifa in midweek.
Both sides return to Champions League action on Tuesday before Juventus travel to Torino for the derby next Saturday, while Milan visit Verona on Sunday.
Eder Militao's early header gave Real Madrid a low-key 1-0 win at Getafe to move them back to the top of LaLiga.
Real moved on to 22 points, three ahead of rivals Barcelona, who have a game in hand and will host Celta Vigo on Sunday.
Militao scored the winner in the third minute, ghosting between several defenders to head home from close-range from a corner by Luka Modric.
Getafe have lost two straight games and are 16th on seven points, two above the relegation zone.
Meanwhile, Angel Correa scored twice as Atletico Madrid won 2-1 against Girona.
Both Correa's goals were scored in the early minutes of each half. The Argentinian stroked in a close-range, first-time shot from an Antoine Griezmann cross to open the scoring after five minutes.
It was Atletico's second consecutive La Liga win as they looked to rebound from their Champions League loss to Club Brugge on Tuesday.
They will face the Belgian side again in Madrid on Wednesday, with Atletico sitting last in Group B on three points, six behind the Belgians who are top.
Ligue 1 leaders Paris Saint-Germain played more than one half with 10 men but salvaged a goalless draw at Stade de Reims to extend their unbeaten run this season.
Sergio Ramos picked up a straight red card as tempers flared shortly before half-time but a reshuffled PSG, in the absence of the injured Lionel Messi, managed to keep a clean sheet.
They have 26 points from 10 games and lead Marseille, who slumped to a 2-1 home defeat by AC Ajaccio, by three points. Reims are 14th on eight points.
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