A couple of late goals from the midfielder ensured the visitors' spell at the top of La Liga was short lived.
A tepid game only came to life in the closing stages when a cross from Verza beat goalkeeper Dani Aranzubia and ended up finding the top corner of the capital side's net.
Rather than provoking a reaction, more poor play from the shot-stopper saw him dismissed and from the resultant penalty Verza sent midfielder Gabi -- who took over in goal for the closing stages -- the wrong way.
The result leaves Atletico on 57 points, level with Real Madrid, which goes top on goal difference.
Atletico coach Diego Simeone was without key trio Thibaut Courtois, Luis Filipe and David Villa for the trip to Andalucia, all of whom missed out with injuries.
Fresh from a 3-0 derby disappointment against Real on Wednesday in the Copa del Rey, Atletico looked determined from the off and 19-year-old right back Javi Manquillo almost got his first La Liga goal with a chipped effort in the seventh minute, but Angel Trujillo got back to clear.
January signing Diego was the next to go close with a dipping 25-yard effort, but Esteban got his fingertips to it, turning it past the post.
With 28 minutes on the clock, Almeria was lucky to escape without conceding a penalty.
The lively Manquillo once again found himself in an advanced position and on-loan Liverpool midfielder Suso pushed him in the back while challenging the teenager in the air, but the referee ignored the Atletico protests.
Diego narrowly missed the target again early in the second half as he cut across the Almeria area after coming in from the right before unleashing a powerful low drive towards the bottom-left corner, but the left-footed attempt went just wide.
Almeria substitute Helder Barbosa somehow escaped a red card with 24 minutes left as the Portuguese midfielder produced a callous two-footed stamp on Tiago's right leg, resulting in his compatriot being forced off on a stretcher.
The hosts almost snatched the lead as Aleix Vidal jolted past two defenders before seeing his side-footed effort hit both posts, but luck was on their side shortly after as Verza fortuitously found the top corner after Aranzubia misjudged his cross.
Verza completed the scoring four minutes from time as he confidently dispatched a penalty past Atletico captain Gabi, who was forced to go in nets after Aranzubia was harshly sent off for bringing down Zongo.