Chelsea substitute Christopher Nkunku struck in the 86th minute to secure a 1-0 victory at Bournemouth in a game littered with a Premier League record 14 yellow cards on Saturday.
Bournemouth twice struck the woodwork and Evanilson had a first-half penalty saved by Robert Sanchez.
But Chelsea finished the game strongly and Nkunku, who came on in the 79th minute, slotted home from close range to make it two away wins out of two for the London side.
Chelsea moved up to seventh with seven points from four games, while Bournemouth are 11th with five points.