Chris Lines and Matty Taylor goals on the day at the Memorial Stadium, coupled with Taylor's in the first leg, mean that second-placed Bristol will play either Grimsby Town or Eastleigh, who trail 2-1 after the first leg, in the final at Wembley on May 17.
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After both sides had squandered early opportunities, Lines struck the only goal of the game in the 24th minute with an arrow-like shot from 15 yards after Nathan Blissett had cleverly let Taylor's cross run across his body and into the path of his teammate.
Moments later, Taylor almost put the hosts two up on the day as he was denied by Steve Arnold after bursting into the box.
Taylor continued to be Bristol's biggest threat after the break, but Arnold appeared as though he would win their personal battle with several saves.
That was until the 88th minute when Taylor finally got the better of him with a simple finish from Lee Brown's pinpoint low cross.