Jonny and Iago Aspas made the difference for the visitors as they hit either side of Marcelo in a frantic six-minute spell that decided the encounter.
The Swede came to the rescue of team-mate Paul Pogba, who had been cast as the villain of the piece with an awful handball to give away a penalty.
The Uruguayan scored twice while Lionel Messi, Arda Turan and Aleix Vidal were also on the scoresheet as the Blaugrana eased to a comfortable victory.
The usual star man was on show for Mauricio Pochettino's men as they strolled to three points to make it six Premier League wins in succession.
A six-goal thriller at the Sanchez Pizjuan threatened to end the Merengue's incredible unbeaten run, but their French star popped up to earn a tie.
All three members of the MSN were on target to reverse a 2-1 deficit at Camp Nou, with the Argentine swooping to decide the tense tie late on.
The Argentine duo were in fine form to ensure a perfect start to the year for the defending Serie A champions, who remain in pole position for yet another Scudetto.