Plea scores hat trick for Gladbach
"It looks like a lot, feels like it, too," Bayern coach Niko Kovac said of the gap after his side's best performance in weeks. "But in football everything is possible."
Reus missed good chances to score, but Alcacer, who came on with half an hour remaining, scored in the 73rd minute after Axel Witsel split the Bayern defense with a perfect through ball. The Spaniard stayed cool in front of Manuel Neuer to score his eighth goal in his sixth league appearance.
Bayern president Uli Hoeness and chairman Karl-Heinz Rummenigge, watching in the stands, were drenched in beer by the home fans.
Lewandowski, who'd had a goal ruled out for offside, had an injury-time equalizer ruled out through VAR, again for offside.
Dortmund, which had a four-point lead, moved seven points clear of Bayern and stayed four clear of second-placed Borussia Moenchengladbach, which defeated Werder Bremen 3-1 away.
Former Augsburg 'keeper Marwin Hitz made his league debut for Dortmund after regular No. 1 Roman Buerki dropped out with a thigh problem.
Bayern made a promising start, displaying characteristics rarely seen since September — tenacity, determination, passion and speed — forcing early corners and pinning the home side in its own half.
Lewandowski broke the deadlock midway through the half with a powerful header to Serge Gnabry's precise cross over the covering defender.
Once the game resumed, Neuer was adjudged to have brought down Reus, who dusted himself off to score the resultant penalty.
Lewandowski grabbed his second minutes later, another header after Joshua Kimmich chipped the ball in.
Reus should have scored again when Jadon Sancho found him completely free, but Kimmich got back with a goal-line clearance for Bayern.
Then Lewandowski thought he'd scored his third, but the goal was ruled out for offside.
Reus finally equalized shortly after Alcacer came on. The Spaniard, who starred in come-from-behind wins over Augsburg and Bayer Leverkusen, was to prove the hero again.
"We have to correct a lot of things. There's a huge amount to improve," Dortmund coach Lucien Favre said.
PLEA HAT TRICK
Alassane Plea earlier scored a hat trick for Moenchengladbach to win in Bremen 3-1 and consolidate second place.
French striker Plea, Gladbach's record signing after arriving from Nice in the offseason, grabbed three goals in a 13-minute spell either side of halftime.
Fortuna Duesseldorf ended its six-game losing streak in the league with a 4-1 win at home over 10-man Hertha Berlin. Maximilian Mittelstaedt was sent off for a second yellow card in the 41st, and Takashi Usami opened the scoring early in the second half.
Also, Stuttgart ended Markus Weinzierl's three-game losing start as coach with a 2-0 win at Nuremberg; Hoffenheim beat Augsburg 2-1; and Mainz won at Freiburg 3-1.