The Merseysiders, holding a 1-0 lead from a fortnight ago, were without the injured Steven Gerrard (toe) and Jamie Carragher (rib) and manager Rafael Benitez opted for Javier Mascherano and Mohamed Sissoko in central midfield with Argentinian winger Sebastian Leto making his debut on the left.
Before the game, moving tributes were paid to murdered 11-year-old Rhys Jones, with his parents standing on the touchline as both Everton's Z Cars theme tune and Liverpool's You'll Never Walk Alone theme tunes were played.
Liverpool opened the scoring on 19 minutes as Benayoun and Kuyt combined to create a chance for Crouch to turn in at the far post.
After halftime, Mascherano's powerful run to win a corner on the right set up Liverpool for their second on 49 minutes, Hyypia unmarked to head home from eight yards from Benayoun's centre.
Kuyt gained his reward for a night of constant running by drilling home the third off the far post after 87 minutes, and then forced in his second in injury-time.