The visitors took the lead just before half time when Javi Marquez stunned his former club with a low but powerful strike from 35 yards, which caught out Francisco Casilla.
Espanyol had a strong period of possession just after the restart, capped off by the home side winning a penalty after Samuele Longo was brought down in the area, Verdu stepping up to take the spot kick and level the scores.
Mallorca played the final 10 minutes a man down, after Antonio Luna saw red for a second bookable offence.
It took Espanyol just two minutes to take advantage of their extra player, Raul Baena slotting the ball home from close range for their third goal of the game.
The victory moves Espanyol up to 14th in the La Liga table and away from the relegation zone, while Mallorca remain in the bottom three.