Messi was at his best at RCDE Stadium in Barcelona, getting past defenders with ease and effortlessly putting his teammates in a position to score.
But he impressed the most on free kicks.
The first came in the 17th minute from about 25 meters (yards) away. Messi curled a left-footed shot into the top corner, with the ball turning away from the outstretched arm of Espanyol goalkeeper Diego Lopez.
"I try to follow a ritual, to repeat what worked the first time," Messi said. "Luckily both shots went in. Sometimes I try several free kicks and don't score any goals."
The second came in the 65th, with the ball a bit further back and from a slightly different angle. Messi's shot was struck just as perfectly at the first one, curling over the wall and into the top corner. This time, Lopez didn't even get close to making a save.
"We all know what Messi is capable of," Barcelona midfielder Sergio Busquets said. "He is crucial for us, taking free kicks or just playing. That's why he is the best player in the world."
Messi had also set up Dembele's goal in the 26th, sending a well-placed throughball to the French forward. Dembele got rid of a defender with a nice cut-back move before sending a high shot into the far corner.
Dembele gave the assist for Suarez's goal just before halftime, with the Uruguayan's shot from a tough angle finding the net after going through the legs of Lopez.
Oscar Duarte appeared to have scored Espanyol's lone goal in the 73rd but it was judged offside after a lengthy video review.
It was the fourth straight league loss for Espanyol, which dropped to ninth in the standings.
Barcelona has won four in a row in all competitions.
SEVILLA SETBACK
Sevilla missed a chance to stay close to Barcelona by conceding in stoppage time against Valencia.
Pablo Sarabia had given Sevilla the lead from close range in the 55th, but French defender Mouctar Diakhaby equalized for the hosts with a header two minutes into added time.
"We had kept our focus until that last play," Sarabia said. "We had it under control until then."
Sevilla was coming off another 1-1 draw at Alaves.
Valencia moved to 13th, seven points clear of the relegation zone.
ATLETICO KEEPS PACE
Nikola Kalinic, Antoine Griezmann and Rodrigo each scored a goal in Atletico Madrid's 3-0 win against fourth-placed Alaves.
The result ended the team's run of two consecutive draws in the league.
It was the third loss in five league matches for Alaves.
Kalinic opened the scoring from close range after a right-side cross by Santiago Arias in the 25th minute at Wanda Metropolitano Stadium. Griezmann added to the lead on a counterattack in the 82nd and Rodrigo sealed the victory in the 87th.
Atletico defender Lucas Hernandez had to be substituted in the 36th with a right knee injury. He was replaced by Jose Maria Gimenez, who returned after missing five matches because of injury.
CELTA SURVIVES
Celta Vigo opened a three-goal lead and then held on to a 3-2 win over Villarreal after conceding twice in the final 10 minutes.
Villarreal, which was coming off an 8-0 rout of second-division team Almeria in the Copa del Rey, stayed 17th in the standings, just outside the relegation zone.
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