Jürgen Klopp’s side trailed by a single goal at the interval, with Jonathan Walters’ header at the near post a minute before the break giving the home team an advantage to fight for.
The visitors had failed to create any genuine chances to that point and the manager was prompted to make a double substitution, Philippe Coutinho and Roberto Firmino entering the action from the bench.
He was rewarded with a wholesale change in performance level and after Coutinho equalised on 69 minutes, Firmino slammed a sensational finish into the roof of the net moments later to grab three precious points.