The young attacking duo accounted for all three goals as hosts repeated their first round success with a victory over the leaders.
Amid a first-half chess match, Marco Reus scored into an empty net to put the hosts ahead on 14 minutes. Patrick Herrmann made it a two-goal lead shortly before halftime, and completed his brace on 71 minutes.
Bastian Schweinsteiger, in his first competitive game since early November, pulled a goal back in the 76th minute, but it was too little, too late for the visitors.
The game was tightly played in the opening stages, but as in his team's Bundesliga opener in August, Neuer was guilty of giving a clear chance to the hosts. Off his line, the goalkeeper passed the ball directly to Reus, who collected and fired home from distance.
After going ahead, the hosts dug deep and greatly limited their visitors' chances: a well-placed Mario Gomez header on the quarter hour mark was Bayern's only clear opportunity of the half, and Marc-Andre ter Stegen did extremely well to parry it wide.
Gladbach looked dangerous on the break, and doubled its advantage four minutes before halftime as Mike Hanke, who on another occasion fired narrowly wide, slotted a brilliant through ball to Herrmann, who coolly finished when one-on-one with Neuer.
The visitors had no spark at the start of the second half, and Gladbach continued to punish the increasingly exposed Bayern. Roman Neustadter failed to complete a pass in a two-on-one counterattacking situation, but Gladbach nonetheless was very rarely put under pressure. Philipp Lahm played a clever 1-2 with Toni Kroos, but the defender was denied a shot on goal as a last-ditch challenge resulted in a corner.
With 19 minutes left to play, Herrmann put the result to rest as he latched onto an inch-perfect through ball from Reus, rounded Neuer and made it 3-0. Schweinsteiger pulled one back on 76 minutes after a chaotic stint in the Gladbach penalty area, but his effort was no more than a consolation goal.
Bayern fought to the very end, but - Schweinsteiger's goal aside - was foiled by a resolute defense that was without the suspended Dante.
The result sees Gladbach climb to second in the Bundesliga table, just a single point behind leader Bayern. By Sunday, Dortmund and Schalke could draw level on points with the Bavarians, but barring a miracle, the first-placed side will not be surpassed.