Heung-Min Son's goal midway through the second half was enough for Leverkusen to move to within 10 points of Bayern, who face Nurnberg on Saturday, and become only the second side after Bayern to win in Monchengladbach.
The hosts, who dropped only two points inside their Borussia Park Stadion in the entire first half of the season, let another three slip to remain a point behind Schalke, who are in action on Sunday.
Gladbach started the game better and a Patrick Herrmann volley tested Bernd Leno.
Max Kruse had a shot deflected over as only the home side did any attacking at all until five minutes before the interval.
Stefan Kiessling saw Leverkusen's first shot of the night saved by Marc- Andre ter Stegen before Son blazed a shot over from 25 yards.
Gladbach continued to set the tone of the game in the second half, but after losing possession cheaply in their own half, Leverkusen broke.
Sidney Sam squared for Son, who was given too much room on the edge of the area to curl his shot beyond a forlorn ter Stegen.
The hosts responded well and threw caution to the wind, although they did not get any closer than a Juan Arango effort which Leno pushed away to safety.
It was Lucien Favre's 100th game in charge of Gladbach, but not one he will look back on fondly.