The Uruguayan was the star for Luis Enrique's side as they got the win they needed to secure a second consecutive domestic crown in the final game of the campaign;
Barcelona have defended their Liga title after a hat-trick from Luis Suarez secured a 3-0 victory over Granada on Saturday.
Real Madrid's victory away to Deportivo La Coruna was not enough as Barca sealed a comfortable victory to achieve a final points tally of 91 - one more than their fierce rivals - and claim a 24th top-flight crown.
Suarez tapped in Jordi Alba's low cross to give Luis Enrique's men the lead, becoming the first player other than Lionel Messi or Cristiano Ronaldo to score 38 goals in a single Liga season since Hugo Sanchez in 1989-90.
Any tension within the Barca camp was eased even further when Suarez headed in from close range just before the break, although they had Marc-Andre ter Stegen to thank for a strong save shortly after half-time which maintained their comfortable advantage.
Granada, who secured their survival with a shock 4-1 win away to Sevilla last week, produced a far more committed performance in the second half but were lucky not to be reduced to 10 men when the officials failed to spot Miguel Lopes push his head into Neymar's face.
Barca - not helped by an injury sustained by Javier Mascherano - found themselves under increased pressure but showed resilience to hold on to the advantage.
Suarez then netted a late third to end the league season with 40 goals, with the final whistle greeted by wild celebrations from the bench and the visiting support in the upper tier of Los Carmenes.
Barca thought they had snatched an early lead, but the officials judged that Andres Fernandez had done just enough to keep Gerard Pique's header from crossing the line.
Lionel Messi stung Fernandez's fingertips from distance and Pique was again thwarted with a header, but any mounting nervousness was quelled as they found a deserved breakthrough on 22 minutes.
Neymar's brilliant return pass sent Alba clear inside the area, and his cut-back was tapped in by the unmarked Suarez for one of the easiest strikes of his prolific season.
Barca looked relaxed in the Granada sun and took another step towards the title seven minutes before the break. Mascherano's raking long pass was hooked back across goal by Dani Alves and Suarez raced in front of Fernandez to steer a header into the net.
Granada responded in the second half and only a save from Ter Stegen denied Fran Rico a lifeline after he raced through the sleeping Barca backline, though Fernandez produced an even better stop to claw Neymar's low effort away from the bottom corner at the other end.
Lopes' rash response to a foul on Neymar went unpunished, but tempers flared once again when Granada refused to put the ball out of play as Mascherano went down in the centre cirle before receiving lengthy treatment on the sidelines.
Luis Enrique had looked pensive on the bench but he led the rapturous celebrations when Suarez slotted home after Neymar's unselfish square pass in a fast break with four minutes to go, as the cries of 'campeones' echoed down from the fans above.
