As they have done so often this season however, Leverkusen scored late, Stanisic’s goal coming from a corner deep into added time.
It was Leverkusen’s 14th goal to come after the 90th minute this season and kept their dreams of becoming the first team to go unbeaten through a Bundesliga season alive.
“It’s not easy to play when you’re already champions, but we challenged ourselves to stay unbeaten this season and that’s our goal,” Leverkusen midfielder Granit Xhaka told DAZN.
Leverkusen have enjoyed another excellent week, following securing the German title by seeing off West Ham to reach the Europa League semi-finals.
“I feel good — almost as good as last week,” Leverkusen coach Xabi Alonso said.
“To score like that at the end was very emotional and to celebrate right in front of our fans. Not losing… it’s nice.”
Both sides looked heavy legged from their midweek European ties, with Dortmund having reached the Champions League semi-finals with a thrilling win over Atletico Madrid.
Neither side managed to carve out a clear chance in the opening half, with Alex Grimaldo for Leverkusen and the hosts’ Marcel Sabitzer going closest.
With under 10 minutes remaining, Fuellkrug put Dortmund on track to do what no other team has managed to do this season.
Sabitzer lofted a cross across the face of goal to Fuellkrug, who rocketed a volley past Leverkusen goalkeeper Lukas Hradecky and into the back of the net.
Alonso brought on Victor Boniface in search of a late goal and the Nigerian was shown a red card for his involvement in a scuffle, but it was overturned by VAR.
Late in stoppage time, Dortmund goalkeeper Gregor Kobel saved a Grimaldo free-kick, leading to a corner which was headed in by Bayern Munich loanee Stanisic.
The draw leaves Dortmund two points behind fourth-placed RB Leipzig in the race for the final guaranteed Champions League place, although the exploits of Germany’s teams in Europe look set to snare at least a fifth spot for the Bundesliga.
Dortmund travel to Leipzig next week and will be missing Ian Maatsen and captain Emre Can, who picked up yellow cards, through suspension.
In Sunday’s late game, Mainz drew 1-1 at Freiburg to lift themselves out of the relegation spots for the first time since August.
Jonathan Burkardt levelled things up for the visitors after Michael Gregoritsch’s early strike, sending Mainz into the safety of 15th and pushing Bochum into the relegation play-off spot.
© Agence France-Presse
Photo: Twitter @FarizioRomano