The midfielder struck the only goal of the game on 76 minutes following an indirect free-kick inside the Granada area which was wrongly awarded for a backpass.
Referee Ignacio Iglesias Villanueva then further angered the home crowd at El Nuevo Los Carmenes by sending off Odion Ighalo for dissent.
The result means Espanyol are still unbeaten after four games and move up to fifth in the Primera Division table, while Granada remain on four points, in 10th place.
The game took a while to get going, with Espanyol closing down their opponents with great success, but unable to create chances.
The first moment of drama arrived after half an hour, when Espanyol goalkeeper Kiko Casilla came out to gather a cross from Fran Rico, spilled the ball, then scrambled to retrieve it right on the goal line.
A minute later, David Lopez had the visitors' first effort, heading over the bar following a free-kick from Simao Sabrosa.
Brayan Angulo gave Espanyol a scare early in the second half, cutting inside from the wing to shoot at goal, but his effort went wide.
Raul Rodriguez then squandered a golden chance to score, heading over unmarked following a corner.
With 18 minutes remaining, Fran Rico was inches away from striking the winner from a free-kick, his shot just dipping over the bar.
Then Espanyol were awarded a free-kick inside Granada's area, after goalkeeper Roberto Fernandez picked up what the referee had judged to be a backpass from Fran Rico, which in reality was a weak shot from an Espanyol player which had deflected off the Granada midfielder.
Nonetheless, Lanzarote produced the perfect finish after receiving a lay off, curling the ball in off the post to leave Roberto stranded.
Granada almost responded immediately, as Riki ventured up the pitch but could only hit his shot onto the near post from a tight angle
Substitute Ighalo was then sent off 17 minutes after coming on, picking up two successive bookings in the same minute for protesting about time wasting by Casilla to the referee.
With five minutes to go Lanzarote came close to sealing the points, Roberto pushing his shot just wide of the post, the opportunity arising due to the hard work down the left hand side by Thievy Bifouma.