Dortmund remained three points clear after its attack of Jadon Sancho, Marco Reus and Alcacer ran riot with the trio all claiming first-half goals.
Before kick-off, Dortmund's sports director Michael Zorc revealed Borussia is set to make Alcacer's loan stay from Barcelona permanent.
The Spaniard demonstrated why with his 11th goal this season for Dortmund and Spain to become the league's joint top-scorer.
Fresh from making his senior England debut, Sancho, 18, put Dortmund ahead on just three minutes when he fired home after Reus' shot was deflected onto his path.
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Reus then made no mistake with his second chance for his fifth league goal of the season.
Alcacer made it 3-0 after 25 minutes when his sublime chip beat the Stuttgart goalkeeper.
The host tightened its defence after the break, but Dortmund deserved the win as Maximilian Philipp slammed home its fourth six minutes from time.
“That was a big start from us, coming back from the international break,” said Sancho.
“We came out sharp and I was happy to be able to get the first goal.”
Werder Bremen later went second in the table, knocking Bayern down to third, after midfielder Maximilian Eggestein scored either side of half-time in its 2-0 win at Schalke.
Elsewhere, England junior international Reiss Nelson, on loan from Arsenal, scored twice as Hoffenheim warmed up for their Champions League game at home to Lyon with a 3-1 win at Nuremberg.
RB Leipzig is fourth after a goalless draw with Augsburg cost it a fourth straight win.
Brazil defender Felipe was Hannover's hero, then villain after scoring its second goal, but was then sent off in its 2-2 draw at Bayer Leverkusen, for which Karim Bellarabi scored a late equaliser.
On Friday, Serbia striker Luka Jovic, 20, became the youngest player to score five goals in a Bundesliga match as Eintracht Frankfurt romped to a 7-1 win over bottom side Fortuna Duesseldorf.
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