The Scottish manager's future remains in severe doubt after reports of disagreements with owner Vincent Tan, and Suarez, who signed a new long-term deal on Friday, made it 10 goals in four games to ensure Cardiff's woes continued on Saturday.
In what could prove to be Mackay's final game in charge, Suarez put Liverpool in front with a volley from outside the area after 25 minutes and then turned provider for Raheem Sterling three minutes before the interval.
There was enough time for Suarez to grab a third, his 29th Premier League goal of the calendar year, before the break to put Liverpool firmly in control.
Cardiff showed fight in the second half, with Jordon Mutch reducing the deficit just before the hour mark, but it was not enough as their winless away run in the top flight was extended to six games.
Perhaps unsurprisingly, Brendan Rodgers made no changes from the side that beat Tottenham 5-0 on Sunday.
Suarez retained the captaincy after scoring eight goals in his previous three games.
The visitors made just one change from their 1-0 success over West Brom, with Aron Gunnarsson replacing Fraizer Campbell, who dropped to the bench.
Suarez was first to threaten with a shot that clipped David Marshall's side netting after two minutes as the hosts applied early pressure.
Craig Noone had Cardiff's first effort, forcing a save from Simon Mignolet following a quick counter after 16 minutes.
However, Suarez eventually broke Cardiff's resolve when he produced a superb volleyed finish to Jordan Henderson's cross, capping off a magnificent team goal.
Liverpool came close to doubling their advantage seven minutes before the interval when John Flanagan almost turned a Glen Johnson cross past Marshall from a tight angle.
Sterling added the second with his third goal in four games, tapping Suarez's pass into an open net, before the Uruguay international again struck to complete his brace.
After a neat backheel from Henderson, Suarez curled an effort past Marshall and into the right-hand corner of the net for his 19th goal of the season.
Following a low-key start to the second half, Mutch pulled a goal back for the visitors - heading home unmarked from Guy Whittingham's delivery after 58 minutes.
It ended a run of 498 minutes without an away Premier League goal for Cardiff, who were much improved after the interval.
But a comeback never looked likely and Suarez was only denied a hat-trick by the width of a post as the hosts climbed to the summit.
