Rhian Brewster halved the deficit from the spot, although it was not enough to prevent Liverpool from suffering their first defeat since returning from the summer break.
Despite the hot conditions, Liverpool went straight onto the front foot, but the Premier League side soon found themselves trailing when indecision in the penalty area allowed Alcacer to find the top corner from eight yards out.
Liverpool provided a positive response with Joel Matip heading marginally wide from a corner, while Ryan Kent was denied by a terrific save from Marvin Hitz at the back post after a powerful run from Alex Oxlade-Chamberlain.
Hitz also had to be alert to stop Wilson from lobbing him on the edge of the area, and Divock Origi helped keep Dortmund on the back foot with a low drive from distance.
However, Liverpool finally found their equaliser 10 minutes through Wilson, who calmly slotted the ball into the bottom corner from 10 yards after a clever dummy from Kent.
While Liverpool boss Jurgen Klopp avoided the temptation of making alterations at the break, his Dortmund counterpart Lucien Favre made eight, and it proved to be a decision which would ultimately lead to Dortmund taking control of the contest.
Their second goal came as a result of some poor defending, with Thorgan Hazard's low cross from the right-hand side of the penalty area being turned in at the back post by Delaney.
Dortmund extended their lead just five minutes later as Bruun Larsen was teed up around eight yards from goal, before the playmaker found the far bottom corner with a low effort.
Adam Lewis was the pick of the players and the left-sided youngster contributed to Liverpool winning a penalty with 16 minutes left, with Ben Woodburn the player to eventually be pushed over in the box.
Brewster took responsibility for the spot kick, proceeding to fire the ball into the roof of the net with a confidence which could have only impressed his manager.
Both sides continued to push for goals during the final stages, but only a last-gasp volley from Andrew Robertson came close to earning Liverpool a deserved share of the spoils.
BORUSSIA DORTMUND (4-3-3): Hitz; Piszczek (Morey 46'), Hummels (Pherai 80'), Toprak (Balerdi 46'), Guerreiro (Schulz 46'); Weigl (Witsel 46'), Gotze (Reus 46'), Reyna (Wolf 46'), Brandt (Bruun Larsen 46'), Sancho (Hazard 46'), Alcacer (Delaney 46')
LIVERPOOL (4-3-3): Mignolet; Clyne (Alexander-Arnold 60'), Matip (Van Dijk 60'), Gomez (Lovren 60'), Larouci (Robertson 60'); Fabinho (Henderson 60'), Milner (Lewis 60'), Oxlade-Chamberlain (Wijnaldum 60'); Wilson (Jones 60'), Kent (Woodburn 60'), Origi (Brewster 60')body check tags ::