Two Steven Gerrard penalties were enough to see off a spirited performance from the Hammers, who had equalised through Guy Demel on the stroke of half-time.
The victory means Liverpool have now won their last nine league games, remaining unbeaten since the turn of the year.
They welcome Man City to Anfield next Sunday and Rodgers believes his side can conquer their title rivals.
"I think it was interesting to hear (City captain) Vincent Kompany say we were the best team they have played," he said.
"The team we have put together, the mentality is to be fearless.
"It doesn't matter who we play, we have to respect them because they have world-class players but it is about ourselves and the confidence we have to play, there is no pressure on them."
The crunch game, as well as all of next weekend's fixtures including both FA Cup semi-finals, will kick-off seven minutes late in tribute to the 25th anniversary of the Hillsborough disaster.
The inquest into the reasons why 96 Liverpool fans lost their lives back in 1989 is also ongoing and Rodgers believes it is fitting that the Reds are once again challenging at the top of the league at a time when those supporters are remembered.
"I think it is brilliant that people are talking about the football of Liverpool," he added.
"The supporters are so happy with how they are seeing their team play.
"We can't say too much on Hillsborough because the inquest is under way but as a manager I knew coming into the football club that there are 96 people in the sky that will always be supporting this team.
"We want to do it for the great support and the football family of Liverpool and if we are to achieve anything this year they will always be in our thoughts."
A positive result at home to Manuel Pellegrini's side will no doubt make Liverpool the favourites to win their first league crown since 1990 after Gerrard's penalty brace wrapped up three vital points in east London.
West Ham boss Sam Allardyce was aggrieved by referee Anthony Taylor's performance, and especially irritated by his decision to award the pivotal second spot-kick, but acknowledged that Liverpool are right in the hunt for the Premier League trophy.
"We wouldn't like to be talking about the decisions and the officials but unfortunately it seems to crop up rather too regularly," he said.
"They (Liverpool) have got a good chance now but obviously the key factors are probably the Manchester City and Chelsea games at home.
"Can they hold their nerve in those games? If they play and score as many goals as they have been recently, apart from against us here, then they can but who knows?
"It will be very, very tight at the bottom and very, very tight at the top."