The Argentine, who holds the La Liga and Champions League scoring records, produced a now familiar devastating performance to take his record to 402 goals for Barca in all competitions, including 28 in friendlies.
Messi produced his tour de force just a day after Cristiano Ronaldo, his rival for title of world's best player, scored a La Liga record 23rd hat-trick against Celta Vigo in a 3-0 win for leaders Real Madrid.
The win left Barca in second place in La Liga, two points behind Real.
Messi may have two fewer La Liga hat-tricks than Ronaldo but he has 29 to the Portuguese striker's 27 in official matches for their Spanish clubs.
Former Barca player Sergio Garcia put Espanyol ahead at the Nou Camp but Messi, who had earlier hit the crossbar with a free kick, equalised before halftime, his landmark 400th goal coming with a clinical strike from the edge of the area.
Shortly after the break, Luis Suarez found the Argentine and he again hit the corner of the net from a similar distance.
Espanyol were in disarray and Gerard Pique was allowed a free header from a corner to add to the lead after 53 minutes.
Substitute Pedro latched onto a long ball from Jordi Alba to grab another and, with nine minutes remaining, he set up Messi for a brilliantly executed third.
"Until the first goal the game was at a slow tempo which is what we are used to as rivals just pack the defence," Barca coach Luis Enrique told a news conference.
"When we conceded, the doubts came and we couldn't find an end product to our play. The key came with the goal before the break and then after that it was all a lot easier."
David Moyes, the former Manchester United manager, suffered his first defeat as coach of Real Sociedad as they were crushed 4-0 at Villarreal.
The floodgates opened in the second half after an Enaut Zubikarai own goal, with Denis Cheryshev adding another before a late double from Moi Gomez.
Valencia’s Champions League hopes took a further blow as they were held 1-1 away to Granada and lie fifth on 25 points.
Alvaro Negredo scored his first goal in a Valencia shirt but the visitors were then reduced to 10 men with Paco Alcacer sent off in the 86th and Isaac Success grabbed an equaliser two minutes from the end.
(Editing by Ian Chadband/Alan Baldwin)
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