Earlier, Cristiano Ronaldo rounded off a week where he was named World Player of the Year for the third time by scoring twice as Madrid struck three times in the final half hour to beat Getafe 3-0.
Atletico Madrid, who dumped Real out the Copa del Rey in midweek, moved back to within four points of their city rivals in third as goals from Mario Mandzukic and Raul Garcia handed them a 2-0 win over managerless Granada.
“Messi has been at an extraordinarily high level all season,” said Barca boss Luis Enrique, despite reports of a dressing room rift between the two in recent weeks.
“He hasn’t dipped at any point. He has been world class.”
In a change from his much criticised rotation policy, Enrique named the same side that beat Atletico 3-1 at home last weekend and was rewarded with another bright display illuminated by Messi’s class in front of goal.
The Argentine’s first effort of the game was brilliantly saved by Fabricio after a well-worked corner, but the Deportivo goalkeeper was helpless when the four-time World Player of the Year opened the scoring after 11 minutes with a thunderous header from Ivan Rakitic’s cross.
Messi then showed a more subtle touch for his second with a delicate chip over the prone Fabricio to double Barca’s advantage from Neymar’s pass.
However, by contrast, Luis Suarez’s troubles in front of goal continued as he fluffed his lines twice in the first-half with just Fabricio to beat.
Messi showed the Uruguayan how it should be done once more when he rounded off his 30th hat-trick for the club after the break when he cut inside onto his favoured left foot and fired into the far corner before an own goal from Deportivo defender Sidnei rounded off the scoring.
Real had to wait over an hour to make the breakthrough at the Alfonso Perez Coliseum before Ronaldo fired home from Karim Benzema’s wonderful assist to set them on the road to victory.
“It is true at the start we didn’t play with a lot of intensity,” said Real boss Carlo Ancelotti.
“At the start we played a bit slow, but I liked the performance because the team played with intelligence and much better in the second-half than the first.
“I think the whole team played well, but the assist by Karim (Benzema) opened the game up for us. It was extraordinary.”
After a sluggish start the European champions were denied by a series of fine saves by Getafe goalkeeper Jordi Codina either side of half-time, whilst Toni Kroos also struck the bar just before the break.
However, Codina’s resistence was finally broken just before the hour mark with a brilliant team goal as Isco and James Rodriguez combined to free Benzema and the Frenchman produced an exquisite piece of skill on the byline to cut the ball back for Ronaldo to slam home.
Just four minutes later it was 2-0 as this time Rodriguez was the provider with a fine low cross that Gareth Bale prodded past Codina with the outside of his left foot.
And another sumptuous cross from Rodriguez 11 minutes from time allowed Ronaldo to plant a firm header past the helpless Codina to register his 36th goal of the season.
Atletico were less impressive as they laboured to victory against a Granada side that hasn’t won in La Liga since September leading to the sacking of coach Joaquin Caparros on Friday.
The opening goal arrived 11 minutes before half-time when Diego Godin was hauled down by Abdoul Sissoko as he tried to reach Fernando Torres’s cross and Mandzukic smashed home the resultant penalty for his 16th goal of the season.
Atletico enjoyed more control of the game after the break and finally sealed the points three minutes from time when substitute Garcia bundled home Arda Turan’s cross at the back post- AFP