PHOTO: AFP
Espanyol held the European champions 0-0 in a bad-tempered first of three meetings between the sides in 10 days at the weekend and threatened an upset early on through Felipe Caicedo's composed finish.
Yet, Messi took just four minutes to restore parity before blasting a stunning free-kick in off the underside of the bar just before half-time.
The Argentine teed up Gerard Pique for a third and then Neymar for a sensational volleyed finish two minutes from time to hand Barca a commanding advantage ahead of the second leg on January 13.
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However, Messi was lucky to escape without being seriously injured after being violently stamped on by Espanyol goalkeeper Pau Lopez without any action taken by the officials before Hernan Perez and Papakouli Diop were dismissed.
Arda Turan was handed his Barca debut after joining from Atletico Madrid in July as the Catalans' year-long ban on registering new players came to an end on Monday.
Yet, Barca were stunned on nine minutes when on-loan Real Madrid midfielder Marco Asensio robbed Dani Alves and played in Caicedo to slot home.
A wonderful through ball from Andres Iniesta ensured the lead was short-lived as Messi fired past Lopez.
When Messi and Barcelona conquered all
And there was little the 'keeper could do to stop a bullet of a free-kick from fully 30 yards.
Brilliant passes from Iniesta and Messi then teed up Pique for an easy finish to all but kill the tie off.
Espanyol lost their cool in the final quarter as Lopez somehow escaped with a blatant stamp on Messi inside the area before Perez and Diop were sent-off in a four-minute spell.
And Neymar finally made the visitors pay when he volleyed home first time from Messi's scooped pass.
Elsewhere, Alvaro Negredo scored a hat-trick as Gary Neville enjoyed just his second win in seven games in charge of Valencia with a 4-0 thrashing of Granada.
"We are going in the right direction," said Neville.
"We are better physically, in our play and our confidence, but obviously we have a long way to go and we can't get carried away with just one win."
Athletic Bilbao produced a stirring second-half comeback from 2-0 down to take a 3-2 lead into the second leg of their last-16 tie against Villarreal.
The visitors counter-attacked to perfection before the break to take a commanding lead through Leo Baptistao and Samu Garcia despite resting a host of first-team regulars to prioritise their push for a top-four finish in La Liga.
However, Inaki Williams's early strike after half-time brought last year's finalists back into the game before Aritz Aduriz came off the bench to score his 22nd goal of the season and Aymeric Laporte rounded off the comeback 10 minutes from time.
Sevilla took control of their tie in the first of three derbies on Wednesday as goals either side of half-time from Michael Krohn-Dehli and Grzegorz Krychowiak handed them a 2-0 win at Real Betis.
Mirandes, one of only two sides from outside the top flight left in the competition, maintained their hopes of reaching the last eight as Alberto Lopo's late equaliser rescued a 1-1 draw for Deportivo la Coruna.
La Liga leaders Atletico Madrid also face a derby later against Rayo Vallecano.
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