Coutinho drifted inside from the left and held off two defenders outside the area before rattling the ball in off the far post with a venomous shot, breaking the deadlock in the 57th minute.
The league's top scorer Lionel Messi started the game on the bench but replaced Coutinho in the 67th minute. Iniesta was substituted in the 82nd, hugging most of his team mates as well as some Real Sociedad players and the referee as he left the Nou Camp pitch for the last time as a Barca player.
They continued to sing Iniesta's name long after he had gone off the pitch. The captain returned with his team mates after the final whistle to lift the club's 25th Liga title and also show off the King's Cup trophy which they won in April, beating Sevilla 5-0 in the final.
"Today is a difficult day. I have spent 22 marvellous years here and I've been so proud to defend and represent this badge, which for me is the best in the world," Iniesta said, addressing the Barca fans from the pitch.
Barca end the season on 93 points, 14 more than second-placed Atletico Madrid and 17 above last year's champions Real Madrid. Ernesto Valverde's side lost only one Liga match, last week's 5-4 defeat at Levante.