Sebastian Dubarbier opened the scoring in the 14th minute, while Verza doubled the lead just before the half hour mark from the penalty spot after Diego Mainz had fouled Fernando Soriano in the area.
Riki went closest for the visitors, with the former Deportivo La Coruna striker denied by the crossbar after the interval, before Alex Vidal sealed victory for Almeria 11 minutes from time.
It was their second success in a row and ensured a happy return from the winter break as they moved four points clear of Osasuna, who play Espanyol on Sunday.
On-loan Braga midfielder Helder Barbosa headed off target as the hosts looked to gain the ascendancy in the early stages.
They earned it after 14 minutes when Argentinian midfielder Dubarbier coolly finished past Granada goalkeeper Orestis Karnezis from Vidal's right-wing cross.
Soriano hammered over from close range although the 34-year-old atoned for his miss by winning a penalty after he was fouled by Granada captain Mainz in the area.
Verza made no mistake in the 28th minute, slotting low to his left to leave Karnezis with no chance.
Almeria goalkeeper Esteban was called into action just before half-time to protect his side's two-goal advantage by tipping over from Yacine Brahimi's strike from the edge of the area.
Fran Rico also headed over as Granada ended the half strongly and they had a great chance to halve the deficit just after half-time as Riki's header from Brahimi's cross cannoned off the bar.
Soriano was denied by Karnezis with Vidal shooting tamely over on the follow-up as Almeria looked to put the result beyond doubt.
The two Almeria players then linked up well to do just that in the 79th minute as Soriano played in Vidal to score from close range and ensure Francisco Rodriguez closed the gap on Granada to just one point.