Die Schwaben had their chances, but an Ivan Perisic brace as well as goals from Robin Knoche and Kevin De Bruyne proved decisive as Dieter Hecking's men moved up to second in the standings courtesy of their fifth Bundesliga win on the bounce.
With league leaders FC Bayern München not in action until Saturday evening, Wolfsburg went into the game knowing victory would take them to within a point of the Bundesliga summit. After a shaky start in which Diego Benaglio did well to keep out Stuttgart lone striker Martin Harnik, the in-form Wolves got their noses in front when Perisic profited from a mix-up between Oriol Romeu and Antonio Rüdiger to calmly slot under Thorsten Kirschbaum.
Armin Veh was seething, but the hosts almost got themselves back on level terms through Christian Gentner, who would have expected to do far better than fire straight at former Stuttgart custodian Benaglio from ten yards. Wolfsburg responded with another incisive route-one move of their own, as veteran Croatian striker Ivica Olic went within a crossbar's width of his fourth league goal of the campaign.
De Bruyne on song
Stuttgart continued to give as good as they got offensively with Sercan Sararer planting a downward header against the upright, but their defensive foibles once again proved their undoing late in the half. Olic had a close-range effort chalked off for offside, before Knoche ghosted onto the end of Kevin De Bruyne's wonderfully weighted free kick to put the Wolves firmly in the driving seat.
Wolfsburg's Belgian midfield maestro followed up his sixth assist of the season with his first Bundesliga goal since 10 May early in the second half. Vieirinha's right-wing cross was measured to perfection and, unmarked at the back post, De Bruyne applied the finishing touch for his fourth goal in as many appearances against the crestfallen hosts.
Stuttgart deserved credit for the way in which the acquitted themselves in the face of a near-impossible challenge, but there was to be no fairytale comeback akin to last weekend's astonishing 5-4 victory over Eintracht Frankfurt. Benaglio, for one, was in no mood to be beaten, the Swiss stopper saving well from Rüdiger to keep the Wolves' clean sheet intact.
Indeed it was that fine piece of goalkeeping that effectively put an end to any lingering optimism inside the Mercedes-Benz Arena. Olic went close, before De Bruyne teed up Perisic for his second of the afternoon to rubber-stamp Hecking's 100th win as a Bundesliga head coach with three minutes left to play.
Line-ups and statistics