Suarez bagged a brace and an assist for Raheem Sterling to put the Reds 3-0 ahead, but Cardiff grew into the game in the second half and pulled one back for Jordon Mutch, before Liverpool closed the game out.
The home fans thought Liverpool had opened the scoring almost immediately when Suarez got on the end of Joe Allen's cutback, but the Uruguayan could only find the side-netting after escaping the attentions of a lacklustre Cardiff defence.
Liverpool were enjoying plenty of joy going forwards, but almost suffered a sucker-punch when Craig Noone escaped down the right wing and cut inside Mamadou Sakho, but his curling effort was too central and Simon Mignolet managed to push it away.
In the end, the visiting defence could only hold out so long. The team and player to get the first goal were little surprise as Suarez celebrated his new contract by opening the scoring, crashing home a crisp volley from the edge of the area into the bottom corner, with Marshall left with no chance.
Cardiff had been playing reasonably well up until that point, but crumbled afterwards - some awful positioning left Suarez with the freedom of the left flank to collect Jordan Henderson's trap and spring clear of the visiting defence, squaring for Sterling to tap in a simple finish and double the hosts' advantage.
Suarez was looking in unstoppable form, and more or less wrapped up the game just afterwards, curling home a brilliant effort into the top corner from Henderson's backheel to continue a remarkable record of goalscoring and leave the Reds well in control.
Cardiff did not look to have improved too much after the break as the hosts continued to create a string of chances against the beleaguered Bluebirds. As might be expected, Liverpool were showing a touch of complacency and Sterling, Coutinho and Henderson all had efforts from range with teammates better-positioned, and Marshall not unduly tested by any of them.
The visitors then managed to sneak a goal back from a set-piece, taking advantage of some poor Liverpool marking as Mutch, who was one of the few Cardiff players emerging from the match with some credit, headed home a looping free-kick to make it 3-1.
Cardiff couldn't have looked less likely to make the contest competitive, but remarkably there were a few nerves from the hosts as the visitors began to attack. Steven Caulker went close from a corner, but Liverpool -- not for the first time -- were lucky to escape the already-carded Martin Skrtel attracting the referee's attention for some particularly aggressive holding at set-pieces.
Liverpool then had another chance on the counter-attack through Sterling, but the youngster took too long to get his shot away, allowing Marshall to deny him before Suarez could only find the side netting with his follow-up.
Brendan Rodgers then brought on Daniel Agger, switching to three at the back to see the game out, and Cardiff failed to threaten too much more, despite finishing the game with a ludicrously attacking line-up after Andreas Cornelius had replaced Aron Gunnarsson. Suarez had yet another chance to complete his hat-trick, but curled wide, leaving the Reds with a comfortable win which saw them end the game at the top of the league table.
Liverpool: Mignolet, Johnson, Flanagan (Kelly 55'), Skrtel, Sakho, Lucas, Allen, Henderson, Coutinho (Agger 83'), Sterling, Suarez.
Goals: Suarez 25' 45', Sterling 42'
Cardiff City: Marshall, Theophile-Catherine, Caulker, Turner, Taylor, Medel (Campbell 55'), Gunnarsson (Cornelius 80'), Noone, Mutch, Whittingham, Odemwingie (Bo-Kyung 55').
Goals: Mutch 58'