Iker Casillas produced an excellent stop to keep out Verza's second-half spot-kick at the Estadio de los Juegos Mediterraneos as the hosts passed up the chance to make it 2-2.
That miss was made to look even more costly when Cristiano Ronaldo's amazing season continued with a late brace to give the final scoreline a flattering gloss for Real.
Verza had earlier shown his finishing prowess when his stunning long-range strike in the 39th minute cancelled out Isco's well-taken opener.
The European champions were ahead by the break, though, as Gareth Bale headed home Toni Kroos' cross.
Ronaldo's goals then proved enough for Real to extend the longest winning streak by a Spanish team and the Liga leaders will travel to Morocco to contest the Club World Cup with a five-point gap over rivals Barcelona, who play Getafe on Saturday.
After initially struggling to assert themselves Real grew into the game and in the 13th minute Kroos' excellently controlled volley cannoned off the crossbar via a deflection.
Ronaldo showed the first glimpse of his talent soon after with a marauding run down the left and his cross forced Almeria goalkeeper Ruben to come out quickly to smother Karim Benzema's shot.
Real were largely frustrated in the attacking third by a stern Almeria defence, but the hosts' resistance was broken in the 34th minute.
Benzema's cross from the right picked out Isco at the back post and the Spain international dummied to shoot before cutting inside Michel and curling his effort past the despairing Ruben.
The visitors were caught off guard just five minutes later, though, as Almeria levelled from Verza's expert 30-yard volley that nestled in the bottom right-hand corner.
However, Almeria were not level long as slack defending allowed Bale to head home Kroos' excellent centre four minutes before the break.
Referee Alfonso Alvarez harshly adjudged that Marcelo had fouled Edgar Mendez in the penalty area, but the underdogs could not capitalise as Casillas produced a fine save low to his left from Verza's effort.
Ronaldo, who had endured a frustrating evening to that point, rubbed salt in the wound nine minutes from time when he played a one-two with Benzema and slid the ball into the unguarded goal.
The Portuguese then bagged his 25th league goal of the season in the 89th minute when he drilled home Dani Carvajal's cross from close range.
