Neither side came close to a goal in an evenly-contested first half short on clear-cut chances, but the visitors took only two minutes to make the breakthrough after half-time as Adrian Colunga slotted below Cristian Alvarez from a narrow angle.
The hosts pushed forward in search for an equaliser, but only succeeded in leaving themselves open at the back. Twice they were caught out on the counter-attack as Sporting sealed the points with goals from Oscar Trejo and Mate Bilic in the final 20 minutes.
Sporting remained in the bottom three, but victory boosted their chances of beating the drop with three games to go.
Espanyol manager Mauricio Pochettino had insisted pre-match Los Pericos needed all three points if they were to remain in the fight for a European place, but they seemed sloppy right from the off as Sporting had the better of the opening stages.
Alberto Lora came closest to opening the scoring in the first 45 minutes as his fierce drive from 25 yards was brilliantly tipped over the bar by Alvarez.
The hosts, though, did begin to create chances just before the break as Joan Verdu fired wastefully at Juan Pablo after Coutinho's clever pass found him free inside the area before Ikechukwu Uche should have done better when he headed over from Verdu's free-kick.
Alejandro Galvez also headed just wide at the other end in first-half stoppage time, but Sporting went ahead with the first attack of the second period.
Trejo's ball into the area found its way through to Colunga and he gave Alvarez no chance with a precise right-footed finish.
Alvarez prevented the hosts from falling further behind eight minutes later as he produced a fine save to turn Gaston Sangoy's strike round the post, but there was nothing the Argentinian keeper could do as Sporting doubled their lead with 20 minutes remaining.
Sergio Garcia carelessly lost possession on the halfway line and Colunga's pass put Trejo in the clear to roll home his fourth goal of the season.
And Espanyol's misery was complete 10 minutes later as another ball in behind their defence this time saw Bilic gallop clear and the Croatian kept his head to slot past Alvarez for his second goal in as many games.