Believe it or not, there was a point here when Robin van Persie seemed dangerously close to experiencing the snake-lick of his manager's tongue. The Dutchman had missed a penalty, trying a disguised chip that went horribly wrong, and Sir Alex Ferguson was facing the distinct possibility that Manchester United's 1,000th game on his watch was going to end in something bordering on disarray.

What happened next was nothing short of extraordinary and can be filed, with immediate effect, in the already bulging portfolio of great United comebacks. Van Persie's equaliser arrived after 87 minutes and the game had extended into stoppage time when his header flashed past Kelvin Davis for a hat-trick winner. He had turned the match upside down – devastatingly, and just as Southampton were daring to believe they had their first win of the season.

Football can be brutal and Southampton will know now how unforgiving the Premier League can be for newcomers. They had played with great spirit and togetherness and United were so generous in their defending it would not have been unjust if the home side had been reflecting on a superb victory.

Instead, it became a demonstration of why Van Persie cleaned up with the footballer of the year awards last season and why his new employers were so desperate to beat Manchester City to his signature. The penalty? He will want to watch the replays through the gaps in his fingers and it is doubtful he will ever try that form of chutzpah again. Ultimately, though, that aberration simply reinforced the sense that Southampton had encountered something special.

A lesser footballer might still have been ruminating on what he had done, whereas Van Persie simply set about making sure he rewrote the story again. It was a demonstration of his mentality, as well as his talent for putting the ball in the net, and in both respects he passed with distinction, sparing his team a second defeat in their first three league games.

Nigel Adkins' side deserved the ovation they were afforded at the final whistle. They had matched United, just as they did against Manchester City on the opening weekend, and on this evidence they should not be discouraged about their hopes of staying in the division. To have no points after playing so stoutly must feel galling in the extreme.

Southampton had never displayed any kind of inferiority complex and, at 2-1, there was a 10-minute spell when United were in danger of conceding even more. Rickie Lambert had headed the home side into a 17th-minute lead and Morgan Schneiderlin had exposed more vulnerability in the air to restore the advantage 11 minutes into the second half. Van Persie demonstrated his brilliant, penetrative qualities in between, controlling Antonio Valencia's cross on his chest and lashing his volley past Davis after a slip from the nearest defender, Nathaniel Clyne.

This, however, was a strange day for the deposed champions. Van Persie had squandered another three presentable chances before the penalty and, defensively, it must have been alarming for Ferguson to see how susceptible his team were. Patrice Evra, marking Schneiderlin, was guilty of a slip that was decisive for Southampton's second goal, whereas Lambert's effort stemmed from Tom Cleverley playing a questionable pass to Shinji Kagawa and Schneiderlin, showing great anticipation, stealing in to dispossess the Japan international. Jason Puncheon delivered the cross from the right and Lambert was at the far post, exposing Rafael da Silva's lack of inches with a perfectly placed header.

Schneiderlin was outstanding, while the movement and directness of Lambert, Adam Lallana and Puncheon caused United considerable problems. Ferguson had dropped David de Gea, blaming the talented but erratic Spaniard for one of Fulham's goals at Old Trafford the previous weekend, but Anders Lindegaard's poor kicking on at least five occasions was typical of the encouragement United gave their opponents.

There is something enduringly brilliant about the way Ferguson reorganises his teams when they are chasing games. They had been struggling with 4-2-3-1, with Danny Welbeck on the left rather than a natural wide player. Now they reverted to the 4-4-2 system of old, with Paul Scholes and Nani coming off the bench. Within a minute Scholes had set Van Persie running into the penalty area for a chance he could not convert. Then came the penalty after Davis's poor clearance had gone to Nani and Jos Hooiveld, though connecting with the ball, scythed through the back of Van Persie's legs.

If the penalty chip comes off it can look majestic, as Andrea Pirlo demonstrated against England at Euro 2012. Van Persie's, in stark contrast, could have ruined Ferguson's latest milestone. Except he refused to be cowed. Van Persie pounced on the rebound after Rio Ferdinand's header had struck a post and completed the recovery with a darting run and near-post header from Nani's corner. It was the way he had played himself out of Ferguson's ire that will linger in the memory.

Man of the match Robin van Persie (Manchester United)