The Argentine's stunning free-kick gave Pep Guardiola's men all three points against a well-drilled Atleti team to once again close the gap on their bitter rivals Madrid
Dani Alves scored the opening goal of the game in the 36th minute as the visitors looked good value for their lead at half-time yet Falcao grabbed a leveller four minutes after the restart.
Yet Messi came to the rescue in the 81st minute with a stunning free-kick to give Barcelona all three points against their unlucky opponents who competed well throughout.
The Catalans stay in second place and after Real Madrid's victory over Rayo Vallecano earlier in the da, they now sit 12 points behind Jose Mourinho's side
Barcelona looked lively in the opening stages and thought they had opened the scoring in the eighth minute, only for the goal to be disallowed. Lionel Messi controlled Alexis Sanchez' pass before bypassing two Atletico defenders and pushing the ball past Thibaut Courtois. However, the Argentine was ruled to have used his hand to control the ball in the build-up, earning himself a yellow card in the process - his fifth this season meaning he will miss the side's game against Sporting next weekend.
The reigning Liga champions came close again on 20 minutes through a well-taken set-piece. Xavi stepped up to curl a free-kick 25 metres from goal yet the Atleti goalkeeper was on hand to make a strong acrobatic save to deny the away team the opening strike.
Both teams were difficult to separate in the first period yet the visitors did take the lead in the 36th minute after a smart team move. Dani Alves linked up well with Messi before the attacker slid the ball to Cesc Fabregas to fire across the six-yard line, with Alves waiting to score his second league goal of the campaign.
However, two minutes after taking the lead, Guardiola's men had Victor Valdes to thank for preserving their narrow lead. After some sloppy defensive play by Barcelona, Arda Turan broke into the box before slamming the ball across goal with Radamel Falcao lurking, yet Valdes was sharp enough to intercept it.
Atletico made a superb start to the second period and grabbed an equaliser in the 49th minute. Gabi's corner was unintentionally flicked towards the backpost by Sergio Busquets where an unmarked Falcao was waiting to volley home from six yards, his 20th goal this term in all competitions.
Despite looking anywhere near their best in the second-half, the away side did come within inches of retaking the lead on 67 minutes. Alves' inviting cross was narrowly missed by Messi at the front post yet Alexis Sanchez was on cue to head the ball over the bar.
Just when it appeared Barcelona would have to settle for a point, Messi stepped up with a true moment of magic. The Argentine's free-kick fooled everyone as it curled into the far corner from 25 metres out with Courtois left rooted to his spot - the attacker's 28th Liga goal of the season and arguably his most important.
Next up for Barcelona is a home encounter against Sporting next weekend while Atletico face a trip to Sevilla, hoping to return to winning ways.