Takashi Usami put on a brilliant display before a crowd of 47,829 at Nissan Stadium, scoring a goal in each half for Gamba, with Patric netting the other, as the Osaka side became the first team to win a treble since Kashima Antlers in 2000.
Romero Frank netted for Yamagata, who at least have the consolation of having earned promotion to the J.League first division for next season.
Kenta Hasegawa's men, who also won the J.League and Nabisco Cup titles in their first season back in the top flight, made a slow start and were fortunate not to fall behind when Frank put the ball in the net for Yamagata but was flagged offside.
However, Gamba soon found their stride to strike first when Usami scored his fifth goal of the competition in the fourth minute, pouncing on a rebound to his own shot to open the scoring.
His strike partner Patric doubled the advantage in the 22nd minute with Usami turning provider, leading a break from his own half before laying the ball off to the Brazilian forward to slam into the top corner.
Yamagata fought back in the 62nd minute when Frank caught the defence napping to fire in his first goal of the competition before Gamba capitalised on the space created by their opponents as they surged forward in search of an equaliser.
Usami capped the scoring with five minutes remaining, his long-range shot deflecting off the leg of Takefumi Toma and into the net to kill off any chance Montedio had of completing a comeback.