Diego Godin's own goal on the stroke of half-time and Borja Iglesias' double after the interval lifted Rubi's side to within three points of seventh-placed Real Valladolid, who entertain Athletic Bilbao on Sunday.
Atletico, having watched Barcelona sew up the LaLiga title last weekend, looked very much like a team with little to play for as they slumped to a sixth league loss of the season.
Diego Simeone's men still require a point from their final two fixtures to ensure Real Madrid cannot sneak into second.
Espanyol, without a clean sheet in their 11 previous matches, almost gifted Atletico an early lead.
Diego Lopez denied Alvaro Morata in the third minute after the striker dispossessed Mario Hermoso, who soon returned the favour by cleaning up his goalkeeper's handling error.
Atletico appeared equally vulnerable and fell behind in first-half added time.
Adria Pedrosa burst down the left, skipped past a challenge and saw his cross trickle in off Godin's outstretched boot.
Iglesias doubled the margin in the 52nd minute, racing onto Oscar Melendo's well-weighted ball in behind and beating Jan Oblak from a tough angle.
2 - Atletico Madrid have conceded two LaLiga away goals against Espanyol in a single game for the first time under Diego Simeone. Strangeness. pic.twitter.com/PBQ0GpcKRN— OptaJose (@OptaJose) May 4, 2019
Only Oblak stood between Espanyol and a deserved third as the half wore on, parrying thumping strikes from Sergi Darder and striker Iglesias.
The latter was not to be denied his double. Juanfran stepped across Javi Puado's path in the box and, in the 89th minute, Iglesias dispatched the resultant spot-kick into the top-left corner to complete a convincing victory.
What does it mean? Rojiblancos risking bragging rights
Top spot might be out of Atletico's reach but they still have work to do in order to finish above city rivals Real.
Failing to do the business in the next two matches and leaving the door open to Zinedine Zidane's side is an outcome Simeone will not want to consider.
Pedrosa rippling with potential
Already admired at his boyhood club, flying young full-back Pedrosa further endeared himself to the home fans with a splendid showing against high-pedigree opponents.
The 20-year-old's run for the opening goal was exhilarating and his impressive level of composure was not consistent with that of a player making just his 10th top-flight appearance.
Misfiring Morata becomes anonymous
There have been peaks and troughs in the first part of Morata's loan stint and this was a match to forget.
He failed to score with a good chance in the opening exchanges, made unconvincing contact with a header not long after and then faded out of the contest entirely.
Key Opta Facts
- Atletico Madrid have scored 52 goals after the opening 36 LaLiga games this season, their worst scoring record at this stage since the 2011-12 campaign (50).
- Atletico have conceded the first goal in seven LaLiga away games this term and ended up winless in all of them (D2 L5)
- Atletico conceded two LaLiga away goals against Espanyol in a single game for the first time under Diego Simeone.
- Espanyol have won back to back LaLiga home games against Atletico for the first time since November 2004.