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.
Elsewhere, new Liverpool manager Arne Slot suffered his first setback as his side surprisingly lost 1-0 at home to Nottingham Forest but Manchester City maintained their perfect start to the season.
Forest had not tasted victory at Anfield since 1969 but Callum Hudson-Odoi's 72nd minute curler beyond Liverpool goalkeeper Alisson secured the three points as Nuno Espirito Santo's side moved into the Premier League's top five.
Erling Haaland, whose place in Manchester City's side was in doubt after being granted compassionate leave this week, continued his incredible start to the season with two goals as City recovered from conceding after 22 seconds to win 2-1.
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