Paul Shanley had put the North West Counties League side ahead in the second-half before an unfortunate Joe Denman own goal got West Auckland back on terms.
Wren pulled off a superb save from Harry Bestwick in a sudden-death penalty shootout with Michael Nelson converting the winner to see Wood through 5-4 after a dour 0-0 draw.
In a statement released via social media, North Ferriby confirmed that the Football Association have removed them from the Vase after they determined Niall Tilsley was ineligible to feature against West after receiving two yellow cards earlier in the competition.
2020 Vase Finalists Hebburn Town will travel to either Warrington Rylands or North Ferriby if they can see of Congleton Town in a fifth round tie in the North East on Saturday.
The Wessex League rivals drew 1-1 in normal time with Ben Satterley’s 62nd-minute equaliser cancelling out James Franklyn’s opener for US midway through the first half.
Playing once more at the Coach Road home of the Devon FA as their Bolitho Park ground is undergoing extensive rebuilding work, Parkway were made to fight all the way by a skillful and energetic Clevedon, who battled well and never threw in the towel in this entertaining and fast encounter.
The visitors created the majority of the chances in a tense second half which saw both teams battled hard to keep their Wembley dreams alive. However, neither side could find a way to prevent a penalty shootout.
Despite plenty of chances for both sides throughout, the deadlock could not be broken in 90 minutes and penalties were needed to settle this competitive clash of styles.
The Bears had to wait just two minutes for Johns to latch on to a ball over the top from centre-back Alex Morris, controlling well before slotting calmly past keeper Kieron Blackburn.
Two goals in each half clinched a dominant display for the Northern Counties League Villagers with Jamie Forrester’s penalty and a Tom Corner effort wrapped up by a late double from substitute Danny Buttle.
Two teams who really didn’t need the enforced break as they were flying before Christmas took a little time to settle down and nothing of note happened in the first 15 minutes.
The winner came in the 65th minute after a corner, which seemed to come off Danny Webb for a goal kick, was put straight in from the taker, Ross Adams, drifting over keeper Allen into the far post.
Jack Watts had fired hosts Stourport into a sixth minute lead but two goals from midfielder Sam Fitzgerald had the visitors ahead early in the second half, a lead they never looked like relinquishing.
The history-making Moles were twice forced to come from behind in regulation time through Josh Helmore before goalkeeper Chris Grace became the hero by saving two home spot-kicks in the shootout.
Matwasa celebrated the start of his second spell with the unbeaten Nomads by hitting their first two goals to earn his side a fifth round trip to Walsall Wood next Saturday.
Viney pulled off two brilliant fingertip saves from Josh Robins and Lewis Dan – as the visitors bossed the opening exchanges in search of a killer second goal.