Gary Cahill’s 87th-minute winner had Antonio Conte swinging in delight on the roof of Chelsea’s bench and the captain mobbed by team-mates in front of a delirious travelling contingent.

This was particularly sweet for Cahill as his push on Jonathan Walters allowed the same player to equalise Willian’s opener as the break encroached.

Until Cahill’s intervention Chelsea Chelsea had been heading for two dropped points that would have offered a glimmer of hope to the chasing Tottenham Hotspur and Manchester City. But this smash-and-grab victory will only sap spirits in north London and east Manchester.

Conte hailed the three points as significant, and with Chelsea leading by 13 after 28 matches he was looking at the mathematics, pointing out that the equivalent of seven more victories will guarantee the championship.

“Today was a great win, a good signal but it is important to continue with the same commitment and work rate as a team,” he said. “We need to take 21 points for the title win. There are 10 games to go. I am pleased because to play Stoke at this point of the season, you have to be prepared mentally and physically. For this reason, we won today. It was a tough game, we tried to play football and deserved to win. We faced a really good team.

“I am pleased for Gary Cahill because we conceded a penalty after a little push from him. To score the winning goal is great for him and our team. Diego Costa played very well and showed great discipline. It is not easy to start the game with a yellow card and then to stay calm. Diego is showing me a great will to think and fight for the team. I want to continue this way.”

Costa had a typically spiky afternoon, which did not particularly impress Mark Hughes. “Diego Costa draws fouls and tries to make most of contact – when they are not fouls,” said Stoke City’s manager. “He is adept at the dark arts and everyone in football recognises that. He has many elements and factors, you have to put up with them.”

Stoke started brightly, troubling the visitors along their flanks. This had the home crowd urging them on though N’Golo Kanté’s slick midfield act soon had Chelsea threatening via Marcos Alonso and Costa, whose first half featured a running battle with a variety of opponents.

Costa went down under a Geoff Cameron challenge perhaps too easily, which caused the midfielder to tell him to find his feet again quickly and Blues fans to reel off a few rounds of “Diego, Diego”.

An incident and noise-filled beginning next featured Alonso steaming down the left and when he drew a free-kick Chelsea made the most of the opportunity. This was as soft as goals come. From an acute angle about 30 yards out, Willian struck the ball cleanly but Lee Grant should not have allowed it to squeeze past him at his near right post. He did, though, to cue a Chelsea celebration and some despairing Stoke navel-gazing regarding how, precisely, they were 1-0 behind.

On 32 minutes Stoke started a fight-back. Marko Arnautovic collected a free-kick and his cross claimed a corner. From here the contest took a controversial turn. Bruno Martins Indi finished Cameron’s header-on but, after consultation with an assistant, Taylor ruled the strike out for Saido Berahino either pushing César Azpilicueta or for being in an offside position that interfered with play.

The next incident was the Stoke goal for which Cahill was culpable. Erik Pieters launched a diagonal free-kick from the left into the area and the defender, for some, reason shoved Walters. Taylor pointed to the spot and that was 1-1.

Meanwhile the Costa-versus-Stoke sideshow continued in venomous manner, as a free-kick won by the Brazilian from a Shawcross challenge was followed by Phil Bardsley being shown a yellow card for taking him out. In the second half Costa was relatively becalmed, though he and Martins Indi continued to suggest each might boil over at any moment.

After Alonso crashed a free-kick off the bar, Stoke’s final threat was a late Arnautovic corner that Chelsea dealt with. Now came Cahill’s winner and the feeling they will continue to handle the pressure and claim a fifth Premier League title.

When Taylor blew for full time Bardsley had just been sent off, following a second booking, and Conte and his men greeted their fans’ jubilant singing of “We’re going to win the league” as if they, too, now firmly believe it. As Conte added: “To have a 10-points gap, 13 at the moment [is good], but I like to think our opponents will win tomorrow. We have to look at ourselves. We are happy. We must be ready to fight, today we were ready.”

Hughes has no doubt. “It is Chelsea’s title now,” he said.