Blues boss Frank Lampard dispensed with his 3-5-2 formation and withdrew the luckless Fikayo Tomori in favour of Willian, in a desperate bid to reverse his side’s fortunes.

The changes at first yielded precious little dividend, and just when Chelsea feared another costly loss, up popped Alonso with a vital header.

Pedro forced a parried save from Aaron Ramsdale on the half-turn, and the ever-alert Alonso was first to the loose ball to head into the empty net.

A 10th league defeat of the campaign would have opened the door for Chelsea to drop out of the top four for the first time since October.

Had the Blues lost at Dean Court then Manchester United would have had the opportunity to overhaul Lampard’s men with victory at Everton on Sunday.

While the Blues will be left to lament another frustrating afternoon, at least the visitors were able to salvage a point from the wreckage of a circumspect and at times complacent performance.

Alonso now boasts three goals in two Premier League matches after firing a fine finish in the victory over Tottenham. And the left-back must be praised for fighting back into Lampard’s plans after an extended spell out of favour.

Philip Billing bossed the opening stages as Chelsea cruised dangerously from the off.

The rangy midfielder drew a smart early save from Willy Caballero, but will have been frustrated to fire straight at the Chelsea stopper.

If the Denmark star rued that failure, he must have been as confused as everyone else at Dean Court as to how he managed to blunder a second fine chance.

The 23-year-old picked the recalled Tomori’s pocket to create a one-on-one with Caballero, but could only drag his close-range effort wide of the post.

Caballero saved Chelsea again when batting away Callum Wilson’s point-blank effort, and one warning too many finally saw the Blues shift out of their slumber.

Giroud met Reece James’ teasing near-post cross with a cute backheel that beat Ramsdale all ends up and struck the bar.

The lurking Alonso latched onto the rebound however, and lashed home a clean volley to put the Blues ahead and into control.

Giroud should have doubled the visitors’ advantage straight after the break, but caught Alonso’s cutback under his feet and bungled the ball wide when he should have swept into the net.

By this stage Chelsea considered themselves to be coasting, but were quickly and rudely disabused of any such haughty notions.

Lerma thumped in a header from Ryan Fraser’s corner to level, with Billing’s dummy run dragging Tomori wide to create the space.

And in a flash the Cherries were ahead, the imperious Billing threading a fine inside-right ball for Jack Stacey. The young full-back steadied himself and laid on a cutback of sufficient quality that all King had to do was tap into the net.

A frustrated Lampard responded by hooking Tomori and changing shape from three at the back to 4-3-3, with Willian and Ross Barkley pitched into battle.

James pinged a fine cross but Giroud could only head wide, before the French striker gave way for Michy Batshuayi.

Belgium forward Batshuayi had the ball in the net with almost his first touch, but was comfortably offside from Alonso’s poked pass.

Cesar Azpilicueta fed Pedro on the half-turn as Chelsea’s search neared desperation stakes, and though the Spain winger’s drive was palmed away Alonso was on hand to nod in and pocket the Blues a point.