The celebrations started in earnest seven minutes into the second half when Iniesta capped off a fine move.
Both Barcelona and Sevilla fans sang Iniesta's name when he was substituted in the final stages, with the chants echoing around the Wanda Metropolitano stadium until after the final whistle.
Sevilla responded fairly well, but Barca remained on top and almost got a second when Iniesta struck the crossbar with a left-footed drive from just outside the area. He was slid in down the right of the area with a lovely pass from Messi, before rounding the goalkeeper and scoring on a tight angle.
Barca started the second half rather more relaxed, though they soon clicked back into gear and opened up a four-goal lead. The Argentine profited from a wonderful one-two between Jordi Alba and Iniesta to hammer a finish into the roof of the net.
Barcelona have won their first trophy of the season, after they crushed Sevilla 5-0 in the Copa del Rey.
Ramirez had a chance to grab a consolatory goal in the 62nd minute for Sevilla when he was played through on goal but the on-loan Everton striker shot was stopped by Jasper Cillesson.
With Barcelona preparing to face Sevilla in tonight's Copa del Rey final in Madrid, the atmosphere at the team camp in the Spanish capital was this morning rocked by Mundo Deportivo's revelations over the future of coach Ernesto Valverde.
Coutinho closed the scoring by converting a 69th-minute penalty kick after a handball by a Sevilla defender.
All that was left was for Iniesta's substitution to be given a standing ovation before the captain hoisted the trophy, perhaps for the final time. The first player to achieve the feat was Telmo Zarra between 1942 and 1950 (with eight).
As for Sevilla, they now sit in seventh and are three points off a Europa League qualification place, meaning this will be their last chance of silverware this season after being dumped out of the Champions League by Bayern Munich in the quarter finals. Barcelona now sits pretty at the top of the La Liga table, 12 points ahead of second-placed Atletico Madrid with five games left in the campaign and they are anything but crowned champions of Spain.