The Anfield home crowd feared early that a fourth loss in the last five matches of all competitions was underway for Liverpool at home against Bournemouth.
But after Callum Wilson gave the away team the lead already after nine minutes, Jürgen Klopp's team came together, turned and won the match by 2-1.
The receipt stood for Mohamed Salah in the 25th minute - and a short while later Liverpool also took the lead through Sadio Mané.
The 2-1 victory means the team leads the English Premier League by a 22-point margin down to second Manchester City.
After a phenomenal season for Liverpool, the form has staggered slightly lately with losses against Atlético Madrid (0-1 in the Champions League), Watford (0-3 in the Premier League) and Chelsea (0-2 in the FA Cup).