The visitors needed to win to keep the race alive for another round but, after a sub-standard showing, they succumbed to an injury-time strike from the German forward
Dieter Hecking's men knew that nothing less than victory would suffice if they were to prolong the championship fight for another round but they struggled to create clear-cut openings.
Indeed, Borussia had the better of a disappointing encounter and deservedly clinched all three points in the dying seconds when Max Kruse netted to send the home side above Bayer Leverkusen and into third place in the table.
Wolfsburg were never really at the races and started a game they needed to win in a strangely subdued fashion, with both Alvaro Dominguez and Fabian Johnson going close for the hosts with acrobatic volleys inside the opening quarter.
Gladbach really should have opened the scoring midway through the half when Granit Xhaka put Kruse in behind the Wolfsburg backline with a sublime ball over the top.
Kruse squared for Patrick Herrmann but the latter incorrectly assumed that Diego Benaglio was coming out to intercept and thus checked his run. By the time he realised that the Swiss shot-stopper had decided to stay rooted to his line, it was too late, with a stretching Hermann only managing to poke the ball wide.
Wolfsburg were struggling but they squandered an excellent opportunity in the 34th minute after Gladbach had turned the ball over while on the offensive.
Kevin De Bruyne led the rapid counterattack, feeding the ball out to Nicklas Bendtner on the right-hand side. However, the Dane failed to complete the one-two, allowing Dominguez to clear what should have been a scoring pass for his Belgian team-mate.
Still, Wolfsburg were finally starting to look a threat going forward and they undeniably finished the half the stronger of the two sides, with Ricardo Rodriguez firing a sweetly-struck shot just over the bar seconds before the break.
The interval interrupted the visitors' rhythm, though, as it was Gladbach who made a storming start to the second period, with Herrmann showcasing fantastic technique in testing Benaglio with a half-volley and Wendt shooting over after a lovely one-two with Raffael.
Benaglio was by far the busier of the two goalkeepers at this stage and he went scrambling across his goal in the 62nd minute to ensure that a fine effort from Kruse did not sneak inside his left-hand post.
Kruse continued to look the man most likely to break the deadlock, with the German forward flashing a right-footed volley just wide with 13 minutes remaining, and he was belatedly rewarded for his persistence in injury time when he latched onto a knockdown from Johnson and lifted the ball past Benaglio to put Wolfsburg out of their misery.