They now climb to fifth in the table.
The Barcelona-based side had lost six of their last seven league matches and were unable to find a way past Deportivo early on, but their task was made easier when Pablo Alvarez was shown a second yellow card minutes before half-time.
The home team dominated after that and took the points thanks to fine goals from Ivan Alonso and Joan Verdu in the final half an hour and moved above Athletic Bilbao with the win, with the Basque side away to Getafe on Monday night.
Jose Callejon and Raul Baena missed early chances for the hosts and Depor defender Claudio Morel made a vital clearance to thwart Alvaro Vazquez moments later.
Baena then saw another effort hit the side-netting as Espanyol continued to dominate.
But Depor came closest as Michel struck a shot inches wide six minutes before the interval.
Baena had been off the pitch receiving treatment at the time and Espanyol were briefly reduced to 10 men.
But Deportivo would have to play for much longer with a man down as Alvarez was dismissed for a second yellow card after 41 minutes.
Unsurprisingly, Espanyol dominated after the break, but the locals had to wait until the 61st minute for the vital breakthrough.
It came when Alonso, returning from injury, beat Dani Aranzubia with a brilliant header from David Garcia's cross.
The goal had been coming and there was relief for the home side following their recent woes.
Nevertheless, their advantage remained slim until 10 minutes before the end, when Verdu beat his marker and unleashed an unstoppable angled drive from 15 yards out to confirm an important win for the Catalans.
Espanyol move up to fifth, two points ahead of Athletic Bilbao, who travel to Getafe on Monday.
Deportivo are 14th, still five points clear of the drop zone.