Liverpool started the match brightly and took an early lead through Luis Diaz's first goal for the club. The Colombian winger doubled the lead just two minutes later with a clinical finish.
Bournemouth were struggling to get into the game and Liverpool continued to dominate. Darwin Nunez added a third goal for the Reds in the 37th minute, finishing off a fine move involving Mohamed Salah and Trent Alexander-Arnold.
The second half was a much quieter affair, with Liverpool content to protect their lead. Bournemouth had a few chances to get back into the game, but they were unable to find a way past Alisson Becker in the Liverpool goal.
The win moves Liverpool to the top of the Premier League table, while Bournemouth remain in the relegation zone.
Liverpool 3-0 Bournemouth
Goalscorers: Luis Diaz (26', 28'), Darwin Nunez (37')
Player ratings
Liverpool were deserved winners of this match and they will be pleased with their performance. Bournemouth were disappointing and they will need to improve if they want to avoid relegation.