Brendan Rodgers’ side trailed twice in the first half at the Cardiff City Stadium, but eventually overwhelmed the struggling hosts with another sublime attacking display.
Suarez was the key to Liverpool’s blistering performance and the Uruguay forward now has 28 league goals this season, while Liverpool have scored 18 times in their last five matches.
Defender Martin Skrtel weighed in with two goals, while Daniel Sturridge was also on target as Liverpool stayed within four points of Chelsea with a game in hand over Jose Mourinho’s table-toppers.
Cardiff had led through Jordan Mutch and Fraizer Campbell goals, but by the time Mutch scored again in the closing stages, Ole Gunnar Solskjaer’s team were already condemned to a defeat which left them second bottom of the table and three points from safety.
Rodgers made just one change to the side that crushed Manchester United 3-0 last weekend, with Philippe Coutinho taking over on the left side of midfield from Raheem Sterling.
From Cardiff’s first piece of possession, Steven Gerrard was booked for hauling down Campbell.
Kim Bo-Kyung’s free kick led to a corner and when Liverpool failed to clear, Kevin Theophile-Catherine spooned his shot over the top of Simon Mignolet’s goal.
Liverpool were under heavy pressure early on and in the ninth minute Cardiff were in front.
Fabio and Campbell combined down the right and when the latter fed the ball inside to Mutch, the former Birmingham midfielder beat Mignolet with a crisp strike from 15 yards.
Eight minutes later, the visitors were level.
Showing terrific patience against Cardiff’s rearguard action, Jordan Henderson fed the ball inside Declan John and Glen Johnson’s cross was dispatched with aplomb by Suarez.
Sensing a weakness on Liverpool’s left, Bellamy immediately set up an opportunity for Campbell who headed over from six yards.
Thirty seconds after that, City were celebrating more success down the right.
This time, Campbell cut inside and beat Mignolet with his left foot to make it 2-1.
Cardiff continued to look the more likely with Liverpool’s next best effort being a Coutinho shot from distance that finished closer to the corner flag than David Marshall’s goal.
However, five minutes from half time, Coutinho whipped in a teasing cross that Skrtel volleyed past Marshall from close range.
Eight minutes into the second half and with Theophile-Catherine and Mutch off the field having been treated for head injuries, Liverpool took the lead when Skrtel rose to head home Coutinho’s corner.
Sturridge was becoming increasingly influential and his cross-shot just before the hour mark crashed into the side netting.
Although Rodgers seemed to be encouraging his side to take the sting out of the contest, Liverpool swept forward in search of the goal that would seal the points.
It came in the 61st minute when an audacious back heel from Sturridge picked out Suarez who did the rest from eight yards.
Suarez returned the compliment 10 minutes later with Sturridge beating Marshall from barely three yards after a delightful cross from the Uruguayan.
Mutch snatched an 88th minute consolation but it was too little too late for the Bluebirds.
And inevitably it was Suarez who had the final say when he escaped Juan Cala and side-footed home in stoppage-time.