Diego Simeone's side had to play the whole of the second half with just 10 men after Gabi was sent off on the stroke of half-time, but their defence, which has now kept eight clean sheets in the row at the Vicente Calderon, was rarely troubled by a timid and impotent Espanyol.
The first flashpoint of the game came on 14 minutes.
Diego Costa raced onto a through ball, beating defender Diego Colotto and then, against the odds, Espanyol goalkeeper Kiko Casilla, who brought the Brazilian down outside the area but was only shown a yellow card.
Costa, who was badly missed by Atletico in their two Europa League matches with Rubin Kazan, which ultimately saw them exit the competition, was a constant threat to the Catalans due to his pace and physical presence, and forced the penalty which lead to Atletico's opening goal.
He ran onto a pass by Falcao and was tripped by Hector Moreno. Again Atletico's players appealed for the Espanyol player to be sent off, but referee Carlos Clos Gomez produced just the yellow card. Atletico made the most of the spot-kick though, Falcao sending Casilla the wrong way from 12 yards.
While the game was short on goalmouth action, it was not short on tension.
Six players had received bookings before 40 minutes had been played, and moments before the penalty there was an ugly confrontation involving several players from both sides after Tiago made a late and rash challenge on Juan Forlin.
Gabi and Christian Stuani were both booked for their part in the clash, something the Atletico midfielder would regret shortly afterwards, when he was given another yellow card for a late challenge on Joan Capdevila and sent off.
Javier Aguirre's side had a whole half to get back into the game with an extra man but made little use of their advantage.
Of their 12 shots on goal they only managed to hit the target once, and barely troubled Atletico goalkeeper Thibaut Courtois.
The only real danger came towards the end of the game, when Diego Godin dived in to block a shot by Stuani that was heading towards goal.
If any team looked likely to score, it was Atletico.
An exquisite exchange between Falcao, Costa and Arda Turan deserved to result in a goal, but Tiago's shot was blocked by Diego Colotto.
Costa later on broke free down the left-hand side of the Espanyol half and squared the ball to an unmarked Falcao, but overhit his pass out of the reach of the Colombian.
As the game drew to a close Arda Turan was put through with just Casilla to beat, but his attempted chip was easy for the goalkeeper to stop.
Costa fired wide in injury time and although the nervous home fans were desperate for the final whistle to sound, their victory was never in doubt.