Ruben Suarez gave the hosts the lead from the penalty spot on 14 minutes after Rui Fonte had felled Juanlu in the box and repeated the trick from another spot-kick early in the second half when he was brought down by Jordi Amat, the defender seeing red for denying a clear goalscoring opportunity.
Despite being down to 10 men Espanyol responded as Hector Moreno turned in Walter Pandiani's scuffed shot.
However, Jose Barkero sealed the points with a stunning left-footed effort 15 minutes from time before Espanyol's misery was completed with a second red card, this time for Pandiani as he barged Nano in an off-the-ball incident.
Levante had already had a great week with victories over Real Madrid and Rayo Vallecano in the past seven days and began with an air of confidence as Suarez nearly connected with Juanlu's cross after only three minutes.
Ten minutes later they were in front as Fonte's clumsy challenge on Juanlu gave Suarez the perfect chance to open the scoring, which he took.
Espanyol were the better side for the remainder of the first-half as Thievy, Sergio Garcia and Joan Verdu all saw efforts go just wide of the target.
Just after the break however the visitors had a mountain to climb as Amat pulled down Suarez as he bore down on goal and was dismissed.
The Levante midfielder took responsibility again and although Cristian Alvarez guessed correctly he was unable to reach Suarez's accurately placed shot into the corner.
The visitors got back into the game with 17 minutes to go as Moreno slid in at the back post to turn Pandiani's wayward effort into the net.
However, the hosts restored their two-goal advantage two minutes later when Barkero was given time on the edge of the area to curl a wonderful shot high beyond Alvarez.
Pandiani was then dismissed as he ran into the back of Nano, although the referee indicated he had sent the Uruguayan off for a headbutt.