Eden Hazard’s fifth goal in five games against the Cherries, scored early in the second half, was sufficient to maintain our 100 per cent Premier League record on this ground.
Chelsea were largely on top throughout the game, in the first half especially, when it needed a special save from Asmir Begovic to keep his former side out and Alvaro Morata missed a good opportunity, but we did have to soak up some pressure as the game progressed having missed chances to extend the lead.
However with Cesar Azpilicueta especially strong in defence, the Blues collected our first clean sheet in seven games to move a point behind third-place Spurs.
Antonio Conte made one change to the side which began the win against Watford in our most recent Premier League game seven days ago. He rotated at the back, with Azpilicueta returning from wing-back into the back three in place of Gary Cahill, and with Davide Zappacosta introduced to the team.
Bournemouth were without their top scorer from last season, Josh King, who had not recovered sufficiently from a back injury to play. They did have Jermain Defoe return from a hamstring problem.
This was the first Chelsea game away from Stamford Bridge since the surprise set-back at Crystal Palace. Since then the results had been won two and drawn one, with plenty of goals scored and quite a few conceded too.
In contrast, the opening half of this tea-time match on the South Coast yielded no goals although it was not without its chances, almost all for Chelsea.
Pedro had an early cross cut out before it could reach Alvaro Morata and an attempted through ball by Cesc Fabregas was blocked. Pedro then left Nathan Ake trailing in his wake with a run down the centre but the Spaniard skied his shot when a pass to compatriot Morata might have been the better option.
It was still a promising start from the Blues, clad in our second kit today, and Toni Rudiger’s superbly struck long pass almost created something for the overlapping Zappacosta but Ake intervened.
Bournemouth did stretch the Chelsea defence on 17 minutes but in the end David Luiz made an important challenge at the expense of a corner. Chelsea responded immediately with an Eden Hazard ball to the near post seeking out Morata with a corner again the outcome.
We should have taken the lead midway through the half when Begovic erred badly with a kick, only sending it as far as Hazard. The Belgian spotted and supplied Morata but he paddled the ball wide of the left post with his right foot. It proved to be the best opportunity of the first 45 minutes.
Morata did have the ball in the net soon after when a David Luiz shot was blocked but a marginal offside decision had not gone the striker’s way.
Conte’s men were building up a head of steam, with attacks coming down the right especially where Pedro and Zappacosta’s pace was posing problems. Hazard was popping up either side of the pitch.
Morata skilfully made space for a shot inside the area but was denied by a very good Begovic save.
Bournemouth’s attacks were infrequent but it did need an expert defensive header from Azpilicueta to keep a cross from causing more damage.
Could we make the breakthrough before half-time? Fabregas had two attempts with three minutes to go in the half but both his first and follow-up shots were blocked. Bournemouth generally had plenty of players behind the ball and reached the break level.
The home side started the second half more on the front foot having changed shape but we soon wrestled the initiative back, although the Cherries defence was still looking hard to pick holes in.
Morata, Hazard and Alonso combined for one of our swifter moves but the left wing-back’s ball across goal was too far ahead of Pedro. It was only moments later however that Hazard was presented with the chance to attack down that left side and he made it count.
Morata had battled well in the middle and sent a pass out wide but Hazard was second favourite behind Simon Francis to reach it first. The Bournemouth skipper instead made a hash of his clearance, Hazard was through on goal and he hammered the ball through the gap between Begovic and his near post. Fifty-one minutes gone and it was 1-0.
Having gone ahead, we strangely lost our way a little and a defensive mix-up allowed substitute Jordon Ibe a shot at goal but touches by the stretching Rudiger and Courtois sent it over.
A Hazard shot also cleared the crossbar when Pedro’s pass was played marginally behind his run.
Bournemouth had the misfortune to lose two attacking players to injury during the second half but one who had come on, Callum Wilson, looked poised to test Courtois but for a crunchingly solid tackle by Azpilicueta. There were now just under 20 minutes to go.
Five minutes further on, Conte brought on Danny Drinkwater for his league debut and also swapped his centre-forwards.
Inside the final 10 minutes, Hazard again caused Bournemouth trauma down their right but when he teed up Fabregas, the midfielder from a tight angle lifted his shot over the bar.
Willian was another late sub and he was almost the beneficiary of another poor Begovic kick when the Cherries keeper had come out of his area, but our former player redeemed himself as the two players challenged for the loose ball.
It was the keeper at the other end who was involved in the last significant action of the game, Courtois happily grabbing the ball in the dying seconds when Steve Cook drove one of his side’s best chances too close to the Belgian.
So it was job done down in Dorset with attention turning quickly to a trip to Conte’s homeland and a Tuesday date in Rome.
Chelsea (3-4-3): Courtois; Azpilicueta (c), David Luiz, Rudiger; Zappacosta, Fabregas, Bakayoko, Alonso; Pedro (Drinkwater 78), Morata (Batshuayi 78), Hazard (Willian 84).
Unused subs Caballero, Christensen, Cahill, Ampadu.
Scorer Hazard 51
Bournemouth (3-5-2): Begovic; Francis, S Cook, Ake; A Smith, L Cook, Surman, Daniels, Stanislas (Pugh 63); Afobe (Wilson 73), Defoe (Ibe h-t).
Unused subs Boruc, Gosling, Arter, Mousset.
Booked Smith 59, Francis 88
Referee Craig Pawson