The Trotters drew level prior to the interval, but last season's relegated Bundesliga outfit found three unanswered goals following the restart to condemn their opponents to a second successive Austrian tour defeat.
Bolton, set out in what appeared to be a 4-4-2 formation in the first half, registered their first attempt on goal through Stephen Dobbie's half-volley from 30 yards out soon after.
It was Padderborn who took the lead 21 minutes in, when Marvin Bakalorz stumbled over Amos to earn his side a penalty, which former Hull City man Proschwitz duly converted right down the middle.
The game was slipping away from the Championship side at this stage, and when Marcel Ndjeng found the net from all of 40 yards out, there was only going to be one winner.
There was still time remaining for Idir Ouali to add a fourth a little over 10 minutes from time, as he latched on to a cutback inside the box to pile the misery on Wanderers.