Despite a better display from East Budleigh they departed the Bill Slee Cup thanks to an 89th minute clincher for the away side.
Budleigh took a while to settle, but went close 20 minutes in; Ben Rowland exchanged passes with George Harris before squaring for Josh Whiller whose effort was well saved.
Five minutes later Budleigh were caught out at the back as Bampton took the lead.
As the half wore on Budleigh came more into the game with Hugo Demetre and Liam West driving them on; Rowland saw his shot saved and after a marauding run from Leigh Rice, Harris scooped his effort over the bar.
Budleigh began the second half in similar fashion to the way they had ended the first; Whiller again denied by a fine stop, but on 57 minutes Bampton broke and doubled their advantage.
Substitute Jacob Rice joined the action and almost pulled one back hitting the side netting, but eleven minutes later Budleigh were back in the tie when West stole in to head home a Rowland corner.
In a frantic finish Demetre set up West who saw his shot saved only for Jacob Rice to be denied on the follow up.
Once again the visitors were able to break and snatch a third to go into round two.
This Saturday Budleigh will be looking for their first win when they host Honiton in Division 2. (kick-off 3pm).