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.
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.
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.
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.
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.
