Despite Joe Piggott giving them a first half lead, two goals on the stroke of half time turned the game on its head.
Needing just a point to guarantee second, the Yellows were left at the mercy of results elsewhere, and a late winner for Ashton at Workington means they finish above Warrington in the table.
It now means that Warrington will host Grantham in the play-off semi-final on Tuesday night, with Ashton at home to Farsley.
If Ashton win their semi-final, they will be at home in the play-off final next Saturday, with the winner earning promotion to National League North.
Warrington have now won just two of their last 11 games.
The play-off game at Cantilever Park on Tuesday kicks off at 7.45pm, with tickets £10 adults, £5 concessions and £2 for under 16s.
Stourbridge: Gould, Hayden, Hall, McCone, Pierpoint, Forde, Gallagher, Broadhurst, Benbow, Shearer, Carnat. Subs: Cooke, Christophorou, Hague, Antonio, Hawk.
Warrington: Pilling, Beeley, McEveley, Williams, Higgins, Goulding, Leacock-McLeod, Barnes, Piggott, Bakare, Hayhurst. Subs: Davis, McDonald, Jennings, Makinson, McMillan.