Miguel Angel Moya was sent off for bringing down Riki inside the area early on and Pizzi converted the resulting penalty to give the visitors the perfect start.
However, the hosts were level at the break as Diego Castro also scored from the spot after Ze Castro had upended Abdel Barrada, and when Depor's Abel Aguilar was sent off for a second bookable offence with 20 minutes to go, Luis Garcia's men took full advantage with two goals in two minutes from Alvaro Vasquez and Adrian Colunga.
It had been Domingos Paciencia's side's discipline that had let them down last week as they surrendered a lead against Valencia after having Silvio sent off, but it appeared they would be handed a lifeline in their battle for survival today when Riki pounced on a loose ball inside the area and was brought down by Moya after just 10 minutes.
And even a long stoppage as Jaime Gavilan had to be substituted to allow substitute goalkeeper Jordi Codina to come on did not put Pizzi off as he confidently rolled home his seventh goal of the season.
However, the visitors failed to build on their numerical advantage and gifted Getafe a route back into the game as Ze Castro failed to intercept Colunga's pass towards Barrada and then upended the Moroccan once he was inside the area.
Castro was also secure from the spot to register his fifth goal of the campaign and for the remainder of the first half both sides seemed more intent of getting players from the other side booked than concentrating on the game.
Pizzi and Riki both had headed opportunities to put Depor back in front either side of half-time, but as the game went on Getafe grew in confidence.
Colunga was denied on the hour mark by a fine save from Daniel Aranzubia before Xavi Torres very nearly connected with Colunga's cross after a lung-bursting run.
Aguilar then inevitably became the second player to be ordered off for little more than challenging for the ball in the air with Borja as referee Jose Luis Paradas Romero continued to be card happy, and after Riki missed another gilt-edged opportunity to put Depor in front with a header from Pizzi's cross 15 minutes from time, Getafe took control.
Firstly, Alvaro produced a fine piece of skill to control Barrada's pass on the run before finishing sweetly into Aranzubia's right-hand corner and Barrada was the creator once more two minutes later as Colunga received his low pass into the area before turning and firing high into the net at the near post.
A third consecutive defeat means Depor remain rooted to the foot of the table and four points from safety.