Mason Mount marked his 150th Chelsea start with a fine goal but a badly-needed victory was marred by another injury scare for Reece James.
James had spent the previous 11 weeks recovering from the knee injury that had been picked up on Champions League duty in Milan and ultimately forced him to miss the World Cup finals.
Now Chelsea manager Graham Potter faces another anxious wait to see if the England right-back, who was impressively energetic in the first half, can escape another significant spell on the sidelines.
Kai Havertz opened the scoring on a day when Chelsea were only troubled in the final 10 minutes by a Bournemouth side managed permanently for the first time by Gary O’Neil, freshly elevated from a temporary position by Bournemouth’s new American owner Bill Foley.
The win ended three successive Premier League losses and saw Chelsea reclaim eighth place.
Havertz headed an early Chelsea chance over at the back post and Potter was annoyed a couple of minutes later when Christian Pulisic went down in the box in the act of firing over.
Adam Smith had tugged at the American’s shirt but referee Simon Hooper saw nothing untoward and VAR did not intervene.
Potter’s mood instantly improved when Havertz slid in at the back post to open the scoring in the 16th minute.
Mount’s pass gave Raheem Sterling space on the right to fire a low ball across the box for the German to squeeze under goalkeeper Mark Travers.
Mount doubled the lead seven minutes later with a sweetly-curled low shot from just beyond the D after Havertz had rolled the ball back to him.
Pulisic had the ball in the net only for Havertz to be penalised for a push on Smith and the half ended with Travers making near post saves to deny James and Sterling.
Chelsea were dealt a blow when James was forced off just seven minutes into the second period.
The defender went down in the Chelsea half and although he was able to walk off following lengthy treatment he disappeared straight down the tunnel.
Havertz side-footed wide after superb skills under pressure from Sterling in his own half had allowed the German to cut in from the right.
Travers did well to bat away Mount’s drive before Kalidou Koulibaly nodded a cross from Cesar Azpliicueta, James’ replacement, narrowly wide.
To their credit, Bournemouth did not give up and substitute Ryan Christie forced Kepa into his first save of note 11 minutes before time and Dominic Solanke headed narrowly wide moments before the final whistle.