“You can’t defend against everything and Dortmund have a world-class striker,” admitted Leverkusen coach Gerardo Seoane.
“It was a spectacular game, but it’s annoying when you lead three times and then lose.”
Haaland’s brace in Leverkusen means the Norway striker has now scored eight goals in his last five games for club and country.
Haaland has scored 13 goals this season — five for Norway and eight for Dortmund.
In Leverkusen, teenage Germany international Florian Wirtz put the hosts ahead, then set up team-mate Patrik Schick for their side’s second to make it 2-1 at the break after Haaland had earlier headed Dortmund level.
Haaland then set up Julian Brandt to equalise early in the second half only for Leverkusen’s French winger Moussa Diaby to put the hosts 3-2 up with 35 minutes left.
Dortmund levelled for a third time through Raphael Guerreiro before Haaland coolly slotted the winning penalty into the bottom corner 13 minutes from time after Leverkusen defender Odilon Kossounou fouled Marco Reus.
“I wanted to get to the ball, he made contact. It wasn’t a hard hit, but it hurt, I went to ground. It was a penalty,” said Reus after the VAR had reviewed the action.
The three points were a welcome 45th birthday present for Dortmund head coach Marco Rose ahead of their opening Champions League group game at Besiktas on Wednesday.
However, he was not totally satisfied.
“It was a very wild game, a spectacle. From the coach’s point of view, however, you wish many things were different — we concede too many goals,” said Rose.
Wolfsburg stayed top with a 2-0 win at newly-promoted Greuther Fuerth.
Wout Weghort and Lukas Nmecha scored to leave them as the only team in Germany’s top flight with a 100 percent record — the first time Wolfsburg have started a Bundesliga season with four straight wins.
Later defending champions Bayern Munich can move above Dortmund into second place if they win at RB Leipzig.
