Madrid outfit Rayo held Barcelona to a stalemate at the Nou Camp last week, and on Friday Andoni Iraola's high-energy side took all three points from Barca's city-rivals.
Isi Palazon smacked home the opener from outside the box on 40 minutes, while Senegalese midfielder Pathe Ciss tapped home from a corner on the hour to make it 2-0.
Rayo defender Florian Lejeune was sent off after just 16 minutes after a second yellow card in two minutes, while Espanyol defender Sergio Gomez was red carded for a violent foul on the half hour.
Iraola brought on veteran Radamel Falcao as a late substitute and while lively, was twice caught offside.
Espanyol's Javier Puado hit the post to be denied a consolation goal in the closing exchanges.
Promoted Real Valladolid were just minutes from a first win over Sevilla in 10 years but had to settle for a 1-1 draw.
Anuar gave Valladolid an 80th-minute lead but Karim Rekik equalised six minutes later.
The result gave both sides a first point of the season after Sevilla lost their opener 2-1 at Osasuna and Valladolid were beaten 3-0 by Villarreal.
On Saturday, European champions Real Madrid play Celta Vigo while Barcelona travel to Real Sociedad on Sunday.