It was an extraordinary finale and there might not have been a better goal celebration here since the seismic day Sergio Agüero pulled back his right foot to score the goal against QPR that won Manchester City the league in 2012. Raheem Sterling was at the front of the chase and it was difficult to keep count of the number of team-mates, substitutes and coaches trying to keep up. Even Benjamin Mendy, currently rehabilitating after major knee surgery, was in pursuit, wearing a pink hat and trying to get a selfie.

Sterling ran the whole length of the pitch after the dramatic curled finish, five minutes into stoppage time, to maintain City’s long winning sequence and Pep Guardiola looked close to the point of spontaneous combustion as he hared on to the playing surface, pumping his fists, after the final whistle sounded moments later. Guardiola was so fired up the referee Paul Tierney had to tell him to calm down. Still breathless, City’s manager apologised in the post-match press conference and insisted he had merely been telling Nathan Redmond he was a great player as they came off together. Arms flapping, bellowing in the player’s face, it was a strange form of congratulations.

Those moments will be replayed on television but when everything was done the real story here was that City had saved themselves with one of those moments of late, exhilarating drama that teams tend to look back on at the end of a championship season. It was the third game in a row that Sterling has scored a late winner and his latest intervention made it 19 successive victories in all competitions for Guardiola’s side, including a club-record 12 in the Premier League.

It was difficult not to sympathise with Southampton, who had equalised via Oriol Romeu in the 75th minute, but City should know from all those years of Manchester United dominance that champions have a knack of scoring late winners. It is becoming a habit for City and it means an eight-point lead at the top of the table, with a vastly superior goal difference to add to the equation.

They also showed here that they know how to grind out wins when they are below their best, another useful trait for any team with aspirations to win the league, and if this was a test of their resolve they demonstrated again, as the City fans like to sing, they will “fight to the end”. Can they play more stylishly? Very much so, but that felt like a minor detail after the jubilant scenes at the end. “Mendy’s crazy,” Guardiola volunteered. “He has a six-month injury and he is running like that … disaster!” Yet the manager was smiling, at last, adding that he was too unfit at the age of 46 to join in the chase himself.

Ultimately it will not hugely matter to Guardiola that this was one of his team’s least fluent performances, that Vincent Kompany had a particularly difficult night or that Southampton also had two golden chances to score in the first half, both originating from corners. Wesley Hoedt headed against the crossbar from the first one and Maya Yoshida, inside the six-yard area again, volleyed over when City were caught out again. Mauricio Pellegrino described the manner of Southampton’s defeat as “painful” and the lesson for his players was they cannot be so generous with their finishing at the highest level.

Guardiola had begun the match with David Silva given a rare break, Ilkay Gündogan starting his first league fixture in almost a year and Leroy Sané missing because of a virus. Agüero and Gabriel Jesus found it difficult to link up together and City were fortunate, after their least impressive 45-minute period of the season, to take the lead early in the second half when Virgil van Dijk turned Kevin De Bruyne’s free-kick past Fraser Forster. It was a clear own-goal despite some strange attempts to credit it to De Bruyne.

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Southampton certainly made it a more awkward night than many people might have anticipated, with Mario Lemina catching the eye in midfield and Ryan Bertrand also impressive on the left flank. On this evidence, Forster appears to have recovered from his recent bad spell. Romeu had a splendid game and it was a brilliant touch from the substitute Sofiane Boufal to set up the equaliser. There have not been too many occasions when Fabian Delph has been caught out since he took up his new role as an experimental left-back but this was one. Boufal killed the ball dead, turned away from his opponent and picked out Romeu to fire in a rising shot from 10 yards.

When the electronic board went up at the end of normal time it showed there would be a minimum five minutes of stoppages. And then the ball was at Sterling’s feet with roughly 20 seconds to go and, from a tight space, his shot was curling away from Forster’s dive with just the right amount of bend. Mendy got his selfie and was wearing a daft grin as he limped back to an ecstatic dugout.