Chelsea substitute Christopher Nkunku scored in the 86th minute to secure a 1-0 win at Bournemouth in a game plagued by a Premier League record 14 yellow cards on Saturday.
Bournemouth hit the woodwork twice and Evanilson saw Robert Sanchez save a penalty in the first half.
But Chelsea finished the game strongly and Nkunku, who came on in the 79th minute, scored from close range to secure a second away win from a possible two for the London side.
Chelsea moved up to seventh with seven points from four games, while Bournemouth are 11th on five points.
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While it was not an entirely convincing display from Enzo Maresca's side, who were fortunate in the first half, there were plenty of positives to take away from the south coast.
They ended a 17-match Premier League away clean sheet, handed a debut to on-loan Jadon Sancho, who impressed as a second-half substitute and showed plenty of resilience.
“We struggled in the first half, but in the second half we were much better,” Maresca said. “We didn't win many balls in the first half and that's necessary in this type of stadium against this team.”
However, Bournemouth paid dearly for not taking advantage of their opportunities.
“We had more of everything, more shots, more corners, but in the end what really matters is scoring and they did that in the end,” said Bournemouth manager Andoni Iraola.
A game full of chances and petty fouls looked to be heading for an unlikely draw until Sancho, on loan from Manchester United, played the ball to Nkunku, who showed great strength to turn sharply and tip the ball past goalkeeper Mark Travers.
A game full of chances and petty fouls looked to be heading for an unlikely draw until Sancho, on loan from Manchester United, played the ball to Nkunku, who showed great strength to turn sharply and tip the ball past goalkeeper Mark Travers.
Sancho's goal-scoring role capped an impressive debut for the winger who finished runners-up in the Champions League final while on loan at Borussia Dortmund last season.
“Jadon is a very good player and he can help us,” Maresca said. “Now all the noise around him doesn't matter to me. He is very polite with us, he trains well with and without the ball.”
Bournemouth were better in the first half with Marcus Tavernier's long-range shot crashing off the bar in the fourth minute.
Travers denied Nicolas Jackson at the other end but Bournemouth looked set to take the lead when Brazilian Evanilson was brought down by Chelsea goalkeeper Sanchez in the 36th minute.
However, Sanchez made amends by reading Evanilson's penalty well and keeping his team level.
Chelsea brought on Sancho in the second half in place of Pedro Neto and he showed glimpses of his best form.
But Bournemouth still looked more likely to score, with Sanchez saving Justin Kluivert's shot before Ryan Christie saw his side-footed effort hit the outside of the post.
However, Chelsea weathered the storm and Nkunku sent the visiting fans home happy.
Although referee Anthony Taylor's yellow card made for a hectic evening, most of the cautions were for minor fouls or insults by players towards the referee. In total, eight Chelsea players were booked.
“For me, the number of yellow cards is not a problem. It is what it is. Sometimes the game demands a certain behaviour,” said Maresca.
