Espanyol won a relegation six-pointer at home to Mallorca in La Liga on Friday, clinching a 3-2 win via an 83rd-minute goal to Baena.
The hosts at Estadi Cornella-El Prat led after 16 minutes when Simao found the back of the net, but they were stunned to head into the half-time interval behind.
Mexican attacker Giovani dos Santos equalised 10 minutes prior to the break, before Javi Marquez gave Mallorca fans hope of an escape from the drop zone by putting them ahead seven minutes later.
A penalty to Verdu in the 68th minute squared proceedings, before Baene stole all three points for Javier Aguirre's men with seven minutes of normal time to spare - with the winner coming just moments after a red card was issued to Mallorca attacker Luna.
Espanyol moved four points clear of the drop zone, with Mallorca occupying 18th spot, sitting goal difference from safety.