The Glovers had already recorded their highest ever league position by finishing fourth in the division, and overcame Sheffield United in the semi-finals to set up a tie with Brentford at Wembley.
Striker Paddy Madden gave Town the lead with a beautifully placed shot from outside the area.
Dan Burn made it two on 42 minutes before Harlee Dean nodded home to reduce the deficit after the break.
Yeovil withstood heavy pressure for the remainder of the contest but held on to win promotion to the Championship in their 10th season in the Football League.
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