Second half goals from Roman Martinez, Nicolas Pareja and Nene made it 16 points from 18 for Espanyol who climb four points above the relegation zone.
For Valencia it was a major setback as they missed a golden opportunity to pull away from Villarreal, a point behind in fifth, who lost 2-0 against Sevilla on Saturday.
"Espanyol are on a good run and it is not a coincidence," said Valencia coach Unai Emery. "We had our chances but they defended well and now we have to prepare for our next match (against Real Madrid)."
A few weeks ago Espanyol looked destined for the second division but Argentine coach Mauricio Pochettino has found the magic formula at the right time with five wins and a draw in the last six matches.
"We have beaten a very good team 3-0 but we are going to stay calm because we are still in a difficult situation," said Pochettino.
Atletico Madrid capitalised on Valencia´s slip with a 2-0 win over Real Betis to move a point behind their rivals.
Uruguayan international Diego Forlan scored both goals to take his season´s tally to 25 just two behind the league´s top-scorer Samuel Eto´o.
Deportivo La Coruna are still in with an outside shot of Champions League football defeating Valladolid 1-0 on Sunday to move three points behind Valencia.
New Getafe coach Michel tasted defeat in his first match in charge losing 2-1 to Real Mallorca on Sunday to leave the club staring relegation in the face.
A disastrous mistake from Serbian goalkeeper Vladimir Stojkovic, on loan from Portugueses giants Sporting Lisbon, gifted Mallorca the winning goal on 68 minutes with Aritz Aduriz pouncing on his slack goalkick to slot home.
"At 1-1 the game we were on top and wanted to win it but then this incident (the mistake from Stojkovic) cost us the match," bemoaned Michel.
Last season Getafe were jostling with Bayern Munich in the UEFA Cup and lost to Valencia in the Kings Cup final but they currently lie fourth from bottom.
Getafe sacked Victor Munoz on Monday after three successive defeats but a new coach did not bring a change of fortune.
Michel won six league titles as a player with Real Madrid and is not used to fighting relegation and has little time to adapt with just four games left to save the club from the drop.
Recretivo Huelva scored a crucial late winner to down relegation rivals Osasuna 2-1 on Sunday and are now just a point from safety.
Defender Nasief Morris scored a brilliant volleyed winner in the dying seconds of the match to boost Recre´s chances of staying up. Osasuna stay two points above the bottom three after the defeat.
Sporting Gijon were frustrated by a late equaliser in a 1-1 draw with Athletic Bilbao on Sunday. Incredibly it was Sporting´s first draw of the season and they are now level on points with Getafe who occupy the final safety spot.
Bilbao look to have won their relegation battle and are gearing up for their clash with Barcelona in the Kings Cup final in Valencia on May 13.
On Saturday Barcelona took a giant stride to the title thrashing arch rivals Real Madrid 6-2 at the Santiago Bernabeu to open up a seven point gap at the top with four games left.
"I think Barcelona are a cut above and showed that they were superior," admitted Real coach Juande Ramos.
Barcelona continue their treble bid on Wednesday when they travel to Chelsea for the Champions League semi-final second leg with the first leg finishing 0-0.
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