They survived a scare when keeper Charles Itandje pushed a Salomon Kalou shot wide before almost succeeding with a goal on the break.
Ryan Babel surged towards Chelsea's goal but took too much time to pick out a team-mate and his pull-back was blocked.
But there were signs of the match having more of an attacking edge as the first half progressed and Lampard should have put the home side ahead after 25 minutes.
Lampard was inadvertently put clean through on the Reds goal by Alvaro Arbeloa and seemed set to score only for Itandje to stand tall and block his shot as he tried to dink it in.
Almost immediately, a one-touch passing move on the edge of the Chelsea box gave Lucas a clean sight of goal and his angled shot was well saved by keeper Petr Cech.
Crouch was shown red for his challenge on Mikel
The game quickly reverted to type and the rest of the opening half was a cagey affair with just a Michael Essien strike, which flashed wide, a rare threat on goal.
Essien again went close after the break when a similarly sweetly-struck effort was palmed round the post by Itandje.
Cech came to his side's rescue at the other end after Ricardo Carvalho's tame back header let in Crouch.
The Reds striker tried to chip Cech but the keeper managed to get enough of a touch to stop the ball going in and allow his backtracking defenders to clear.
It proved a vital miss as Shevchenko slipped Lampard in on goal and his shot was deflected in off Carragher.
The Reds suffered another setback before they could regroup as Crouch was sent-off for a reckless challenge on Mikel.
The striker lunged two-footed at the Chelsea midfielder and referee Martin Atkinson had little hesitation in brandishing his red card.
Liverpool carried little threat with 10 men as Chelsea comfortably closed out the game.
Shevchenko sealed the win with his late goal as he powered in a shot from an acute angle after a pass by substitute Michael Ballack.
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