Suarez gave Atletico the lead in the 28th minute with a curling free kick which was cancelled out by Cadiz forward Alvaro Negredo seven minutes later before Saul Niguez restored the visitors' advantage moments before the break.
Cadiz had a strong penalty claim turned down on the stroke of halftime when Atletico's Koke blocked the ball with his hand while on the ground but Atleti got a spot kick just after the break which Suarez converted for his 14th goal of the season.
He has scored five times in his last three appearances and has an average of a goal for every league start he has made.
Negredo reduced the deficit to one goal with a scrappy strike in the 71st and Atletico were pegged back in their area for a long spell while their loanee Ivan Saponjic could have levelled moments later but saw his header tipped away by the ever-reliable keeper Jan Oblak.
Atleti captain Koke then struck his first goal of the season in the 88th minute to complete the 4-2 win and secure an eighth consecutive league victory for Diego Simeone's side.
Atletico have amassed an impressive 50 points at the halfway stage of the season, 10 clear of nearest challengers Real Madrid with a game in hand.
If they can replicate their form in the second half of the season, they will become the first Spanish side to end a campaign with 100 points since Barcelona in 2013.
Cadiz, who have managed to beat Real and Barca this season, slipped down to 13th place.
This was another spirited performance from Alvaro Cervera's side but they failed to take their chances.
Atletico, however, were utterly ruthless, scoring with all four of their attempts on target.