Pizzi hit the winning goal for the Catalans with just a quarter of an hour to play but Malaga could have been awarded a penalty just seconds before when Hector Moreno appeared to acrobatically kick Roque Santa Cruz in the penalty area.
The goal restored Javier Aguirre's side's lead, with Sergio Garica putting the visitors in front in the 32nd minute, only for Pablo Perez to equalise two minutes later.
However, the Argentine midfielder's evening took a turn for the worse when he was sent off just after Pizzi's goal.
The result means Espanyol move on to 40 points and are just six points off a Europa League place, while Malaga still have some work to do before they achieve safety, remaining on 32 points.
Perez fired an early warning shot in just his third start for Malaga since joining in January from Newell's Old Boys, hitting a powerful shot at Willy Caballero when the game was just a few minutes old.
Pizzi then squandered the best chance of the game so far, receiving a low pass from Garcia from a corner, but the Portuguese was unable to keep his shot under the bar.
Malaga's Sergi Darder then tried his luck from range, his shot flying just wide of the top corner.
Espanyol took the lead just after the half-hour mark. Christian Stuani produced a fine piece of skill to beat a defender then played in Garcia down the right hand side of the area and the striker's first-time shot beat Caballero at the near post.
But the hosts responded immediately, Perez receiving the ball right on the edge of the area and shooting into the bottom corner. However, Espanyol's players were adamant the midfielder was in an offside position when the previous pass by Santa Cruz was played.
Espanyol had two chances to take the lead again before the break, Caballero saving first from Pizzi and then the Argentine brought a dazzling run by Sidnei to a halt with a fine save.
The first half had a feel of a basketball match, with one side attacking after the other, but Malaga showed more ambition than their visitors in the second period.
Francisco Casilla had to make a double save just before the hour mark, parrying a powerful effort from Francisco Portillo and then blocking the midfielder's rebounded effort with his legs.
But it was Espanyol who scored next. Garcia raced away towards the Malaga goal and laid the ball off for Pizzi when he got to the edge of the area, the Portuguese hammering the ball low past Caballero.
But Malaga were furious they had not been given a penalty in the run up to the goal for Moreno's challenge on Santa Cruz.
Things got worse for Malaga a minute later, as Perez was then given a second yellow card for an ugly tackle on David Lopez.
Substitute Oleksandr Iakovenko had a final effort for the hosts with five minutes remaining, receiving a pass from Nordin Amrabat, but the Ukranian shot straight at Casilla and was unable to prevent a second consecutive home defeat for Malaga.