Juan Mata levelled things up from the spot half an hour later, however, and after the break the Spaniard's flick allowed Chris Smalling to turn the ball home from close range for what proved to be the winner.
Here, Sports Mole takes an in-depth look at whether the hosts deserved to collect all three points.
On target: 6
On target: 2
Was the result fair?
If either side deserved to win this one tonight, it was United. However, the hosts certainly didn't have things all their own way. The statistics above show that they had more of the ball and more shots than their opponents, but for much of the second half they were on the back foot and hanging on a little. It was almost as if they went into defensive mode as soon as they had taken the lead, despite Smalling's goal coming just eight minutes after the restart.
From that point on it was Wolfsburg asking all the questions, with United's failure to keep hold of the ball seeing their defence come under more and more pressure. Caligiuri, Andre Schurrle, Dante and Ricardo Rodriguez all came close for the visitors after they had fallen behind, but their tally of just two shots on target is evidence that they weren't quite clinical enough in the final third. That said, the skill and movement from the likes of Julian Draxler, Caligiuri and Max Kruse did cause United problems.
Wolfsburg were the better side in the second half, then, but it was United who created the clearest openings before the break. They responded well to going behind, and Bastian Schweinsteiger, Mata, Anthony Martial and Wayne Rooney all had sights of goal before the penalty was awarded. In terms of goalscoring chances, United just about deserve this victory tonight, but on the balance of general play a point apiece would not have been entirely unjust.
Man Utd's performance
After defeat to PSV Eindhoven on matchday one, the most important thing tonight was coming away with all three points. They got off to the worst possible start when they fell behind after just four minutes, and the defending from United left a lot to be desired there. Daley Blind went needlessly chasing after the ball on two occasions to create space in the box, while Antonio Valencia played Caligiuri well onside when he should have been up alongside his fellow defenders in the line.
From that point on, though, United largely controlled things in the first half. They were perhaps a little ponderous in possession at times, not moving the ball quickly enough, but when they did inject a bit of pace and look to get in behind then they created problems for Wolfsburg. The hosts carved out all of the chances from the fifth minute to the 45th, and they probably deserved to go into the break ahead as opposed to just drawing.
It was a sloppy start to the second half from Louis van Gaal's side, though, and they would have been delighted to have relieved some of the pressure with what proved to be the winning goal. It did feel that they may need another to secure the three points as Wolfsburg were looking capable of creating chances, but United went into their shell a little after taking the lead. They didn't offer anywhere near as much going forward as they did in the first half, and towards the end of the match they were simply hoofing the ball clear and could not keep hold of possession. Even so, they held out for the win and that was the big priority this evening.
Wolfsburg may have now lost four from four when it comes to trips to England, but there were plenty of positives for them to take from this latest visit. They could not have wished for a better start to the match, and the slick passing that created the early goal was a sign of things to come. Throughout the match they looked confident in possession and, while they did ultimately only manage two shots on target, they always carried a lingering threat through their attacking midfielders.
That said, they took their foot off the pedal after opening the scoring in the first half, and they were comfortably second best in the opening 45 minutes. Dieter Hecking would not have been too disappointed with his side's display at the halfway stage, but he would have also been aware that they could play a lot better. They did just that in the second half, starting brightly but then falling behind to Smalling's close-range finish following an inventive flick from Mata.
They put United under plenty of pressure in search of an equaliser, but while Kruse and co were pulling the strings, they didn't have a focal point to provide the cutting edge they needed. Bas Dost never really got into the game, and Nicklas Bendtner was unable to make an impact when he came on either. That was all that the visitors were lacking in the end as United hung on to collect the points. Even so, they look like they could be a force in this group and it would be something of a surprise if they don't reach the knockout rounds for the first time in their history.
Sports Mole's man of the match
Juan Mata: Smalling deserves a mention for adding the winning goal to his good defensive performance, but Mata was the most instrumental player for his side once again this evening. The Spaniard was a creative force from midfield and ended the game with a goal and an assist, having also won the penalty that he then dispatched.
This one has got to go to the defending for the opening goal. Blind was drawn out wide and then went chasing the ball rather than guarding his position, leaving Caliguiri in acres of space to collect Kruse's simple through-ball. Even then, though, the Wolfsburg man would have been offside had Valencia not been lurking a good five yards behind the rest of the United line.
Viktor Kassai incurred the wrath of the home fans a few times in the match, and it is fair to say that he made a number of questionable decisions, in addition to handing out some soft cards. He got the big decision right, though, awarding a penalty to United when Mata's cross struck Caligiuri's hand. The Wolfsburg goalscorer would argue that he was too close to do anything about it, but his arm was out and clearly blocked the ball.
Man Utd: It is a big week for United as they take on Arsenal at the Emirates before heading into the international break.
Wolfsburg: Wolfsburg, meanwhile, will be looking to end what is now a three-game winless streak away to Borussia Monchengladbach.