Falcao put Atletico ahead in the first half but, despite enjoying the better of the opening 45 minutes, Diego Simeone's side trailed at the break after a stunning goal from Adriano and a well-taken effort from Sergio Busquets. Messi was a long way from his magical best but still ended up with two goals - his 89th and 90th of a remarkable 2012 - to quell Atletico's challenge in the second period.
It all added up to a wonderful night for Tito Vilanova's men who not only moved a further three points clear of second-placed Atletico at the summit but also took to the Nou Camp pitch moments after arch-rivals Real Madrid had been held to a surprise 2-2 draw by Espanyol at the Bernabeu.
That stalemate left Madrid 13 points adrift of the Catalans - a deficit even boss Jose Mourinho admitted would be "practically impossible" to overhaul.
It looked like being a different outcome in the early stages with Falcao a constant menace to a nervy-looking Barça backline. The Colombia international came within inches of putting Atletico ahead after just nine minutes when he got on the end of Koke's inswinging cross from the right to flick a header on to the inside of the post with Barça goalkeeper Victor Valdes beaten.
Falcao threatened again after 24 minutes but, having been put through by a quickly-taken free-kick by Koke, he dragged his shot across Valdes and wide of the far post.
He did not miss when presented with a third opportunity, however. With 31 minutes on the clock, Diego Costa played in Falcao, whose first touch and explosive pace took him away from Busquets before he clipped a wonderful finish over the advancing Valdes for his 17th league goal of the season.
Barça had mustered nothing in the opening half an hour and it required a moment of brilliance from an unexpected source to drag them level. Adriano picked up the ball on the right flank, cut inside before curling a wonderful, dipping shot past Thibaut Courtois and into the far top corner.
The Atletico defence failed to clear from a Barça corner and after a scramble the ball fell at the feet of Busquets and the Spain midfielder showed great composure to take a touch before firing high into the net.
Second half sees Barça dominate
After holding their own in the first half, Atletico struggled to make inroads in the second as Barça's passing game clicked.
Messi finally got in on the act after 57 minutes by cushioning Alexis Sanchez's drilled pass with the instep before curling a beautiful effort past Courtois from the edge of the area.
Belgian Courtois saved well from Andres Iniesta after 80 minutes but could do little when Messi burst through with two minutes to go, the Argentinian finishing with a trademark clipped lob over the goalkeeper.