Premier League: Liverpool 4 West Ham 1
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 also had skipper Kevin Nolan sent off for a late challenge on Jordan Henderson as their wait for a first win at Anfield for 50 years continues.
Liverpool were without Daniel Agger due to illness, so Sakho made his first Liverpool start for over a month.
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.
Maiga nearly opened the scoring in the 20th minute for West Ham, when Jarvis picked him out with an inviting cross.
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.
Liverpool dominated the first half, but struggled to break West Ham down, with Raheem Sterling wasting a golden opportunity five minutes before the break.
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.
Gerrard was forced off due to injury 10 minutes into the second half, but the home side were in complete control as West Ham struggled to cope with their passing and movement.
Sterling somehow fired over from six yards after Jordan Henderson picked him out 61 minutes in, and then less than a minute later Jaaskelainen made an outstanding reflex save to deny the winger.
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.