A Guy Demel own-goal put Brendan Rodgers' side in front just before half-time and France defender Mamadou Sakho scored his first Liverpool goal just after the break.
Martin Skrtel's own goal gave West Ham hope, but Suarez struck 10 minutes from time for his 14th league goal of the season.
The Uruguayan's shot then deflected in off Joey O'Brien to seal Liverpool's fifth successive home win, a run in which they have scored 20 goals.
West Ham boss Sam Allardyce reacted to his side's midweek defeat at Crystal Palace on Tuesday by bringing in Demel, George McCartney, Modibo Maiga and Matt Jarvis.
The Mali striker's powerful header was bound for the back of the net, only for Liverpool goalkeeper Simon Mignolet to produce a fine fingertip save.
The lively Suarez picked Sterling out with an incisive through ball but the winger lacked composure and his right-foot finish rolled tamely wide, but Liverpool did get the breakthrough in the 43rd minute as West Ham goalkeeper Jussi Jaaskelainen palmed Suarez's shot against the unfortunate Demel and into the net.
Suarez should have doubled the home side's lead soon after, but the in-form striker blazed wildly wide with only Jaaskelainen to beat after great work from Sterling.
The home side doubled their advantage just a minute into the second half as Steven Gerrard's free-kick was met by Sakho and although the defender scuffed his shot, James Collins was unable to keep it out as he desperately attempted to clear.
But West Ham were given a life line as Jarvis headed across goal and Skrtel turned the ball into his own net with 24 minutes to play. Suarez gave Liverpool breathing space with a header 10 minutes from time though, and then Nolan was given a straight red card for a poor challenge on Henderson.
A miserable afternoon for West Ham was rounded off when Suarez's shot deflected in off O'Brien in the 84th minute.
