Los Rojiblancos had suffered back-to-back defeats against Real Madrid and Celta Vigo in recent weeks but made an ideal start at the Estadi Cornella-
El Prat as Federico Fazio and Machin Vitolo put them two goals to the good inside the first 10 minutes.
The home side's captain Sergio Garcia pulled one back midway through the first half but Carlos Bacca restored Sevilla's two-goal lead and it proved decisive.
Espanyol's woeful record shows no sign of abating, with their defeat on Sunday meaning they have now have taken just four points in their last eight games, and their miserable day was compounded when Victor Sanchez was sent off five minutes from time.
A poor start allowed Sevilla to dominate the tempo of the game, almost from the off.
Sevilla captain Ivan Rakitic has led from the front this season with seven goals but he was the provider for his side's third-minute opener.
Having drawn a foul from Raul Rodriguez on the right channel, the Croatian delivered the free-kick and Fazio's glancing header at the near post flew into the top corner.
Worse was to come for Espanyol as they fell further behind in the 10th minute and Rakitic once again had a hand to play in the goal.
His corner from the right to the far post created havoc and Vitolo was on hand to stab home.
The one-way traffic continued and only a magnificent save from Francisco Casilla prevented Rakitic from getting on the scoresheet himself, with the Blanquiblaus goalkeeper turning away the striker's 25-yard effort.
Against the run of play, Espanyol were given a lifeline when Garcia latched on to Simao Sabrosa's pass before turning past Sevilla goalkeeper Antonio Beto in the 23rd minute.
Sevilla then spurned two opportunities to take a two-goal cushion once more as Nicolas Pareja and Daniel Carrico both headed wide from Rakitic set-pieces.
At the other end, Rechel Sidnei nearly levelled for Espanyol after half-time but his close-range strike was fantastically parried away by Beto.
It proved a timely save as Sevilla doubled their lead in the 58th minute.
Sebastian Cristoforo had only been on the pitch four minutes but it was his pass that allowed Bacca to drill low into the net from inside the area.
Espanyol finished the game with 10 men when Sanchez, who had moments earlier been booked for a foul on Cristoforo, received his marching orders for a crude challenge on Vicente Iborra in the 85th minute.