This was billed as a test of Chelsea’s nerve as much as of their quality; they passed it in a way that will seriously examine the strength of Tottenham Hotspur’s belief in the possibility of a collapse by Antonio Conte’s men. Bournemouth were valiant and ensured Chelsea could not simply lounge about in the south-coast sun but the league leaders ultimately subdued their hosts with the imperiousness of champions-elect.

They may need up to 15 points from their seven remaining matches to make it a mathematical certainty but any outcome that does not involve Chelsea claiming the title should probably be filed under fantasy. Not least because Conte keeps warning his players the only way it could become a reality is if they slacken off.

On top of their many other attributes there is, thanks to their manager, a savviness about Chelsea that the teams below them simply do not possess or, in the case of Spurs, seem to have developed a little too late for this campaign.

Furthermore, Chelsea are getting the breaks when it matters, such as when they opened the scoring in the 17th minute. Diego Costa’s miskick led to a slice of good fortune when the ball deflected off Adam Smith and bobbled past Artur Boruc into the net.

Scoring the first goal helped Chelsea to settle after an uncomfortable start. They had marched on to the pitch with the sound of Tottenham’s heavy boot steps clanging in their ears, along with Conte’s order not to be spooked. Any Chelsea player unnerved by Spurs’ pursuit might also have harboured concerns about Bournemouth’s home form. Liverpool, Arsenal and Spurs all endured scares at the Vitality Stadium this season, none having escaped with a win.

What is more, Bournemouth are still fighting for their Premier League lives even if several other teams are more likely victims of relegation.

David Luiz was so flustered by a pinged cross from the right by Ryan Fraser in the second minute he almost shanked it into the net. The Brazilian was grateful for the sharp reflexes of Thibaut Courtois, who batted the ball to safety.

Victor Moses’s return from injury meant Conte could field his first-choice lineup and Moses soon launched Chelsea’s first attack. His cross from the right led to a blocked shot by Marcos Alonso. The Nigeria international tried again in the 17th minute, collecting a long pass by David Luiz before cutting in from his wing to zip a low pass to Costa, who spun past his marker and shot from 12 yards. It was a wonky effort that threatened to embarrass the striker until it took a benevolent deflection off Smith and made its way to the net. Luck like that works wonders against jitters.

Raheem Sterling inspires Manchester City to victory over Hull City Read more

Soon Chelsea swaggered farther ahead and flukiness was not a factor. N’Golo Kanté dissected the home defence with a pass from deep and Eden Hazard skedaddled into the box, duped Boruc into prostrating himself in front of him and then sidestepped the goalkeeper and slotted home. You could almost hear the groans from north London.

There were louder groans from the home crowd in the 29th minute when Charlie Daniels raced behind Moses and crossed for Benik Afobe, whose shot from 12 yards beat Courtois but cannoned out off the post.

Bournemouth though are too strong-minded to lapse into fatalism. They continued working to turn things in their favour and were rewarded just before half-time when King’s shot from 20 yards took a nick off David Luiz and flew into the top corner. Chelsea had food for thought to go with their half-time oranges.

They emerged for the second period in game-management mode, again intent on softening the home side’s bite by hogging the ball. Bournemouth are tenacious and when they finally regained possession in the 50th minute they immediately tried to sink their teeth into Chelsea. A fast-flowing move finished with Fraser firing just wide.

Costa should have restored Chelsea’s two-goal lead shortly after that but failed to profit from six yards after Alonso teed him up for a tap-in.

That attack was a sign Chelsea were back in control and this time they did not look like relinquishing it. From then on Bournemouth were allowed to do nothing more than scamper gamely after Conte’s side as the visitors took command.

Chelsea started to make their dominance look effortless to the point of imperiousness. Alonso confirmed that impression in the 68th minute by curling a sumptuous free-kick over a six-man wall and into the top corner. In theory there was enough time for a comeback but Chelsea played the game out with an authority that made that seem an impossibility.