Espanyol went ahead three minutes before the break courtesy of an Estrada own goal, the Real Sociedad defender turning Alvaro Vazquez's shot past his own goalkeeper.
But Estrada quickly made amends by conjuring up an equaliser on the stroke of half-time.
Espanyol regained the initiative nine minutes into the second half when Sergio Garcia made it 2-1 after Joan Verdu had supplied an inviting cross from the right.
Jose Callejon looked to have put the match beyond Sociedad's reach with a third nine minutes from time after latching onto a pass from Pedro Rui Fonte.
And Javi Marquez put the seal on the home side's win with a fourth on the stroke of full-time curling home a 30-yard freekick.
Real Sociedad had been the first to settle but Antoine Griezmann was off target with his fifth-minute effort and Estrada was wide with another shot on 22 minutes.
The visitors did produce the first genuine threat with David Zurutuza seeing his shot tipped round the post by Espanyol keeper Carlos Kameni in the 26th minute.
Estrada's unfortunate own goal halted their momentum and although he levelled before the break it was all Espanyol after the break.
There were bookings for Espanyol's Ernesto Galan on the half hour and Sociedad's Asier Illarramendi eight minutes into the second half.