In the absence of top goalscorer Marco Reus, Dortmund looked to be heading for a draw before Alcacer scored direct from a free-kick in the first minute of stoppage time, and tapped home a second three minutes later.
The Spanish striker has become a late goal specialist, with 11 of his 16 Bundesliga goals this season coming in the last 10 minutes of matches.
In the eighth minute, Dortmund centre-back Dan-Axel Zagadou headed the first chance of the game just over the crossbar.
Alcacer then came close but his shot went narrowly over after being expertly set up by Mario Gotze, who sent the cross in from the right.
Dortmund goalkeeper Roman Burki made a good save to keep the score level from a deflected Wout Weghorst curled effort towards the top corner.
In a tight first half with few chances, a memorable moment came in the 21st minute when a pigeon nearly collided with the ball and refused to move from the side of the pitch for the remainder of the half.
Jadon Sancho came close in the 62nd minute, forcing Wolfsburg goalkeeper Koen Casteels into his first real save of the game when he fired towards the goal from close range.
In the second half, Dortmund put more pressure on their opponents but struggled to create many clear-cut chances.
Wolfsburg almost took the lead after a good low cross from Jerome Roussillon was deflected across the face of the Dortmund goal and just beyond the reach of Weghorst at the back post.
In the first minute of stoppage time, Dortmund were awarded a free-kick at the edge of the box which was expertly fired into the net by Alcacer.
The Spaniard added a second in the final minute of added time, tapping home from a move started down the right by Sancho to secure all three points.
The news was not all good for Dortmund, with defender Abdou Diallo taken off injured while fellow defender Lukasz Piszczek remains sidelined.