If this was to be Sean Dyche’s last game as Burnley manager, there could hardly be a better time to go. This victory was the sort of performance that would be filed under Dyche’s name in an encyclopaedia, a textbook example of his solid and doughty oeuvre that leaves them outside the Champions League places only on goal difference. Should Everton come calling, Dyche will presumably depart with the best wishes of all involved.

“It’s out of my hands,” Dyche said when the question came. “I just keep getting on with my business, as I have been for five years. The rest of it is noise that’s beyond me. There’s not a story there: my story is the Burnley story. Five years here, another fantastic win, a clean sheet. We’ve won 1-0: that’s the story.”

Indeed. This was not a game for the ages, won by a brilliant late header from Sam Vokes but otherwise light on quality. For the most part Burnley did the stodgy, sensible thing and dug in for the away point but other than the odd spell either side of the break, did not look much like losing.

Southampton tried to have a little more invention but were afflicted with whatever the football equivalent of writer’s block is. Mauricio Pellegrino’s assertion that they were much the better team “in all aspects” apart from one, was a little hard to swallow: that pesky aspect was scoring a goal, which firstly is fairly important but also one the hosts did not really look like managing.

The first save of note either goalkeeper had to make was in the 34th minute, when Sofiane Boufal volleyed towards the near post, but Nick Pope stooped to his right and blocked. A few minutes later Pope tried to inject some entertainment by nearly dribbling straight into Manolo Gabbiadini but basic competence quickly returned and he sensibly cleared.

Southampton’s struggles in front of goal at St Mary’s continued as they failed to break down Burnley’s defence. Photograph: Steve Bardens/Getty Images

It was not that the game was completely devoid of quality – there were a couple of zippy passing interchanges from both sides and Boufal danced out of trouble with a roulette at one point – but it was a distance from being good. At half-time there was virtually no reaction, positive or negative, from the crowd: it was as if 30,000 people were just glad to get out of the house. The game existed, but little more could be said either way.

After the break Southampton dominated possession but Burnley held firm and that was when Dyche displayed one of the reasons he is so coveted when he brought on Vokes and Ashley Barnes, changing the shape, approach and the whole feel of the game.

The switch paid off brilliantly with nine minutes remaining. Johann Berg Gudmundsson collected the ball on the right touchline and boomed over an inswinging left-foot cross to Vokes. The highpoint of the Welshman’s career so far is probably his goal against Belgium at Euro 2016, and this was not a million miles from that: with his body angled away from goal he directed a superb header past the graspingFraser Forster.

“It’s an amazing game, but painful too,” said Pellegrino, painting the picture of a flowing performance unfairly scuppered by some sort of dark arts. The Saints fans who booed their team off, and indeed any objective observer, would disagree.

At the final whistle Dyche applauded the travelling support for perhaps a touch longer than usual. Read into that what you will, but he spoke like a man planning for Burnley’s next game, rather than someone else’s.

“It’s a so far story,” he said. “There are a lot of big teams we’ve got to play. We don’t run away with ourselves, that’s for sure.” Burnley will hope he does not run anywhere.