Second-half goals from Dutch striker Dirk Kuyt and Crouch made it nine wins from 10 league games for Liverpool, who have 49 points from 25 games. Chelsea have 51 and leaders Manchester United are on 57, both from 24 games.
West Ham's Spanish loan striker Kepa Blanco came off the bench to score on his debut in the 77th minute, but the London club remain mired in the drop zone, 18th in the table.
Reading moved up to eighth with a 3-2 comeback win over Wigan Athletic, who are just above the relegation places after suffering a club record eighth league defeat in a row.
Sheffield United moved further away from trouble by beating Fulham 2-0 and Portsmouth finished 0-0 with Middlesbrough in the night's other games.
Liverpool, who had to battle for their FA Cup final victory over West Ham last season, were clearly on a roll after beating Chelsea in their last league outing and made a good start.
West Ham, under new manager Alan Curbishley, soaked up the pressure and finished the stronger of the two sides at the break, creating a couple of chances.
But their hopes were dashed right from the restart, when Liverpool kicked off, went straight up the West Ham end and scored after 10 seconds when Kuyt arrowed a shot in off the bar.
Crouch rounded off a fine passing move by making it 2-0 with a deft 20-metre sidefoot off a John Arne Riise pass soon afterwards and Liverpool looked good for the points despite Blanco's late strike.
Liverpool manager Rafael Benitez, who raised a few smiles from his players by slipping over on the touchline while trying to control the ball, played down the prospect of becoming champions.
"We cannot think about the title," he told the club's Web site (www.liverpoolfc.tv).
"We must just keep on winning and if we do that then in three or four weeks we might be able to start talking about possibilities. We are on a good run and enjoying it."
Crouch told Sky Sports: "It will be difficult, but we've got to keep our run going and hopefully the top two will slip up."
Premier League action continues on Wednesday, when Manchester United host bottom club Watford and Chelsea take on Blackburn Rovers at Stamford Bridge.
