A tight opening period was decided by just the single goal, with Radamel Falcao converting from the spot after 38 minutes.
Both sides had chances in the second half, but neither could make the breakthrough as Atletico held on for a vital three points.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
ATLETICO: Courtois; Juanfran, Miranda, Godin, Luis; Tiago, Gabi, Koke; Turan, Falcao, Costa
ESPANYOL: Casilla; Colotto, Moreno, Capdevila, Forlin; Simao, Verdu, Victor, Lopez; Garcia, Stuani