Messi put the disappointment of losing the World Cup final in his last competitive outing behind him to open the scoring, but Barca were momentarily rocked by Mascherano’s dismissal for denying a clear goalscoring opportunity moments later.
However, 18-year-old Munir El Haddadi made the game safe with a classy lofted finish on his debut a minute into the second-half before Messi rounded off the scoring.
“I have to be delighted with that start,” said Enrique.
“As we expected we had a little bit of difficulty creating chances at the start because Elche are very well-organised defensively, but bit-by-bit we began to find space and opportunities.”
Messi looked back to his best throughout the 90 minutes after his tired showings towards the end of the World Cup and Enrique was in no doubt that he has inherited the best player in the world.
“With Leo playing in his element we have taken the first step and now we move onto the second.
“It is clear that Messi is the best player in the world. He has a unique quality that it is easy to see. Giving assists, scoring goals, pressing, defending he does everything.”
Two goals in Barca’s final pre-season friendly romp over Mexican side Club Leon on Monday had been enough to earn Munir his senior debut in the absence of the injured Neymar and suspended Luis Suarez.
And it was the 18-year-old who had the first meaningful effort of the game as he smashed a shot off the angle of post and bar on 22 minutes.
Barca’s captain for the evening Andres Iniesta then also hit the bar from range as the hosts dominated possession without clearing too many clear-cut chances.
However, Elche were punished for giving away possession cheaply near their own area three minutes before half-time as Sergio Busquets played in Messi and he sidestepped two defenders before slotting home on his trusted left foot.
Minutes later, though, the complexion of the game appeared to have changed as Mascherano was shown a straight red card for clipping Garry Rodrigues as he galloped clear on goal.
Instead, Barca were barely bothered by Elche’s numerical advantage as Munir flicked home Ivan Rakitic’s pass into the far corner a minute after the restart.
Messi then put a seal on a comfortable three points for Barca as he again left three Elche defenders trailing before side-footing past the helpless Vicente Guaita.
Earlier, Eibar made a dream start to their first ever La Liga campaign with a 1-0 win over Basque rivals Real Sociedad in front of a 5,200 capacity crowd.
Javi Lara scored the only goal of the game with a wonderful curling free-kick just before half-time.
And Enrique’s old side Celta Vigo also made a winning start as they beat Getafe 3-1 at Balaidos.
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