Dieter Hecking's men, who sit second in the Bundesliga table, appear set for UEFA Champions League football next season but qualified for the last eight of Europe's second-tier competition on Thursday, for the first time since 2009.
The German side, who came from behind to win last week's first leg 3-1, took a 24th-minute lead through Daniel Caligiuri.
Wolfsburg goalkeeper Diego Benaglio was on top form throughout the contest at San Siro, although he was finally beaten 19 minutes from time by Inter forward Rodrigo Palacio.
But substitute Nicklas Bendtner had the final word for the visitors, lashing in on the turn with a minute to play and ensuring Inter's winless run extended to five matches.
The Italian giants lie eighth in Serie A and have a serious battle on their hands to be involved in any sort of European football next season.
Coach Roberto Mancini kept faith with Juan Pablo Carrizo despite the goalkeeper being at least partly responsible for all three of Wolfsburg's first-leg goals.
Inter - who left Xherdan Shaqiri on the bench as he battles a thigh complaint - saw Hernanes' fierce effort well saved by Benaglio in the fifth minute.
At the other end, Carrizo had to be alert, rushing off his line to claw the ball from the feet of Bas Dost after the forward's heavy first touch.
Mancini called for a rousing atmosphere and the Inter fans delivered as their team began to grow into the game, with Mauro Icardi ballooning over before he drew another good stop from Benaglio.
But Wolfsburg, who remained a threat on the counter, scored a crucial away goal in the 24th minute when Kevin De Bruyne skipped down the left and centred for Caligiuri.
The midfielder's shot hit Carrizo's legs and looped into the net in agonising fashion for the hosts as the Bundesliga team moved three goals in front on aggregate.
Both sides had their keepers to thank as half-time approached, with first Carrizo keeping out an excellent curling Caligiuri effort before Benaglio made himself big to deny Fredy Guarin.
Wolfsburg could have doubled their lead six minutes after the break when De Bruyne broke free but his attempted square ball for Dost was cut off by Carrizo.
The ex-Chelsea man also shot wide, while Inter continued to be thwarted by Benaglio, who made an fine stop with his feet to deny Palacio before Hernanes missed the target.
Inter did get a goal in the 71st minute, as Palacio volleyed in Hernanes' lobbed pass, but Wolfsburg were never in danger of a late collapse and they secured their progression in style as fellow sub Maximilian Arnold set up Bendtner to finish emphatically.
