But it could have been worse for the Reds if Crouch hadn't spared their blushes with a last-gasp equaliser after Villa stunned the Kop with two second-half goals in minutes.
The off-field turmoil surrounding the club's American owners looked to have affected the players as the Reds started tentatively against Martin O'Neill's well-organised outfit.
But after a hesitant start the home side found their game as Harry Kewell carved out the game's first chance on 17 minutes, but his effort was well blocked.
From the resultant corner the Reds took the lead as Yossi Benayoun played a neat-one two with Dirk Kuyt and despite a last-ditch tackle from Martin Laursen the Israeli nipped in to slide the ball home.
Ten minutes later it should have been two, Fabio Aurelio blasted wide after good work from Steven Gerrard and Kuyt
Villa hustled and harried in midfield but couldn't force any real openings as the first half ended as quietly as it had started.
Liverpool sprung out of the blocks in the second half and nearly doubled their lead within seconds of the restart with Laursen nearly turning a dangerous Kewell cross into his own net.
Javier Mascherano then found Gerrard surging forward and the skipper picked out the unmarked Kuyt, but the Dutchman's touch let him down and he fired hopelessly wide.
Benitez's men stepped up a gear and started to hit Villa with a wave of attacks as Kewell, Fernando Torres and Alvaro Arbeloa went close to making it two.
Villa looked a million miles from the side that had gone unbeaten away from home since September but at 1-0 they were still in with a chance as John Carew reminded their opponents with a turn and shot on 67 minutes.
Two minutes later they snatched the equaliser through substitute Marlon Harewood.
The big striker latched on to a Stiliyan Petrov cross to poke the ball past Jose Reina.
Liverpool were stunned but worse was to come as, with the Reds still reeling, Petrov stole in again down the right-hand side and his cross hit the hapless Aurelio and bounced into the empty net.
Benitez sent on Crouch and Ryan Babel in a desperate attempt to turn the match around.
And the England international made an immediate impact as with 89 minutes on the clock he swivelled and buried a shot into the top corner to give his team a lifeline and set up a rousing finale.