The Argentine struck in the first half after ghosting between defenders, before the Ivorian midfielder capped an easy run-out for the Premier League champions
The game was played at a leisurely pace, with a goal five minutes before half-time from Aguero and another 10 minutes after the break from the Ivorian midfielder the only real moments of interest in a simple enough night for City in their final pre-season game before next weekend's Community Shield encounter against Chelsea.
Mancini selected a strong starting XI, with Abdul Razak the only 'unrecognised' first-team member, as Carlos Tevez and Aguero started up front against Edin Dzeko's former club, with the Bosnian named amongst the substitutes.
City's strength told in the early stages, as their 3-5-2 formation dominated possession although failed to force any clear cut opportunities.
In truth, the first half was lacking in any real opportunities for long stretches. Wolfsburg had the occasional shot at goal, but most were from distance and did not trouble Joe Hart.
However, on the stroke of 40 minutes, Aguero opened the scoring. After some patient build-up play, the Argentine broke, gliding between two defenders before poking the ball past the onrushing Benaglio and into the corner of the net.
His strike was the difference between the two sides at half-time, with Hart looking comfortable, and Razak impressing in the centre as he fought diligently to win the ball back, and used it well when in possession.
Marcel Schafer was the first player to come close in the second half, crashing a shot towards Hart's goal on the bounce from outside the box, but with the keeper scurrying, it flew just wide.
Bas Dost was also beginning to exert himself on the match, trying to link up with his fellow attackers. But it was City who scored again only 11 minutes into the second half.
Yaya Toure had just broken through but was deemed offside, yet only a minute later he was in again. Tevez burst through the defence, and just as it looked like he was about to pull the trigger he fed the younger Toure brother, who easily knocked it past Benaglio to double the away side's lead.
The visitors stayed firm with the evening retaining a wholly pre-season vibe; the crowd failed to create any atmosphere, and on the rare occasion that Wolfsburg did create an opening, it was quickly extinguished by City's defence.
Schafer had another long-range effort that Hart did well to deal with, but it was the only real attacking moment of note for the rest of the second half.
There was a relative homecoming, however, for Dzeko as he got a little over a quarter of an hour from the bench, much to the home fans' appreciation.
There was a brief moment of worry for Mancini as Aguero hobbled off following an unnecessary kick from former Middlesbrough defender Emmanuel Pogatetz, but it fortunately it did not look to be too much of a problem, despite his substitution for Roque Santa Cruz.
Mancini then made a few more changes, with youngsters Luca Scarpuzzi and Denis Suarez getting some time on the pitch as the game began to wind down, with Suarez trying to make things happen and raise the tempo somewhat.
But the match ended without any other moments of note, with Mancini's side remaining comfortable in the closing stages as they look ahead to next weekend's season curtain-raiser against Chelsea.