The Reds went behind after a horrible mistake from Dejan Lovren allowed Wassim Ben Yedder to score from close range.
16 minutes later and Liverpool were ahead through Mohamad Salah. The Egyptian's tenacity allowed him to win ball back from Steven N'zonzi, and it paid dividends as his strike fortunately deflected past Sergio Rico.
The Reds were awarded a penalty four minutes later after Sadio Mane was fouled, but Firmino's effort rocketed off the post.
A number of chances were not taken advantage of by the Reds after the Brazilian's miss and they were punished for their inadequate finishing when Correa scored with a lovely finish past Loris Karius.