Messi used a signature burst of speed to dribble free of a pack of opponents before slotting in Barcelona's first goal in the 41st.
Minutes later Barcelona lost Javier Mascherano to a direct red card when he fouled Elche's Garry Rodrigues with only goalkeeper Claudio Bravo to beat.
But Barcelona's 18-year-old Munir El Haddadi, starting for the injured Neymar, scored seconds after halftime before Messi got his second goal in the 63rd after again confounding a group of defenders.
''Leo is one-of-a-kind and today he was in a state of grace,'' said Luis Enrique. ''He will be the best player in the world in every way he wants, defending or attacking.''
Elsewhere, promoted Eibar edged Real Sociedad 1-0 for a winning debut in the first division, while Villarreal won 2-0 at Levante, and Celta Vigo beat Getafe 3-1.
After Barcelona lost its Spanish league title in the last round of last season and Argentina lost to Germany in the World Cup final, Messi summed up his desire for the new campaign to begin by writing on Facebook before the game: ''First match today!!! I hope God is on our side for a great season.''
It started with a bad omen, though: Just seconds after kickoff, the game was paused when a black cat ran onto the Camp Nou pitch before stewards managed to herd it off.
But aside from Mascherano's red card, there was no bad luck for Barcelona.
Messi looked back to his best and his pair of goals seemed the perfect answer to critics who had said the four-time world player of the year had lost a step.
He was lively from the start, both in attack and in defense, and scored his goals in classic Messi fashion: putting the ball on his left boot to breeze around his markers before picking his spot in the opponent's net.
With Neymar out and new signing Luis Suarez suspended until October, Munir got the nod from Enrique and had Barcelona's first chance when he fired the ball off the goalframe in the 22nd.
Andres Iniesta followed suit with a strike onto the crossbar in the 32nd as Barcelona piled up chances before Messi converted.
Sergio Busquets sent an errant Elche pass to Messi, who used four quick touches to open an angle around three Elche players before slotting home his first goal.
Moments after Barcelona grabbed the lead, Busquets' poor back pass forced Mascherano to foul Rodrigues to stop a one-one-one opportunity with Bravo.
Elche failed to take advantage of the extra man and Munir, who had only debuted with Barcelona's ''B-team'' in March, doubled the lead with a skillful tap with the tip of his left boot to float Ivan Rakitic's long pass over goalie Przemyslaw Tyton.
Messi added the third goal despite being shadowed by four defenders, skirting along the edge of the area until he saw the chance to place the ball inside the post.
Rakitic, Bravo and defender Jeremy Mathieu all made debuts for Barcelona after their transfers this summer.
Eibar's first goal in the topflight category was well worth the 74-year-old wait for the more than 5,000 fans at Ipurua Stadium.
Midfielder Javi Lara capped his superb first half two minutes before the break by scoring with a free kick from a tight angle.
Eibar earned two consecutive promotions in as many years to rise from the third to the first division.
Villarreal showed it could compete at the top of the table this season with a dominant performance at Levante, making it the only away team to win through the first eight games of the opening round.
Ikechuwku Uche scored in the 55th, and Denis Cheryshev made it 2-0 in the 85th after he and Moi Gomez had both sent shots off the woodwork.
Luis Enrique's replacement at Celta Vigo, Eduardo Berizzo, also enjoyed a strong start.
Celta forward Manuel ''Nolito'' Agudo beat Getafe goalie Vicente Guaita in the 20th before Fabian Orellano made it 2-0 with a long strike in the 56th. Jorge Sammir pulled one back for Getafe in the 62nd before Joaquin Larrivey restored Celta's cushion in the 70th.