Summer signing Kieffer Moore scored twice as the Red Dragons led 2-0 at half time in their quest for a maiden victory back in the second tier following last season's promotion from League One.
But Wrexham were stunned by second-half goals from captain Barry Bannan and Bailey Cadamarteri as Wednesday demonstrated immense courage in the wake of unbelievable adversity on and off the pitch.
The result means Wrexham sit 19th in the Championship table and are still without a league win, while financially-stricken Wednesday - whose fans continued to call for owner Dejphon Chansiri to sell the club - have climbed up to 21st.
Wrexham, who slipped to a 3-2 defeat to West Bromwich Albion in their last league outing, were aiming for a fast start in front of their home fans and that is exactly what they got when Moore put them in front after just 15 minutes.
Moore, a summer arrival from Wednesday's bitter rivals Sheffield United, reacted first to a loose ball following Lewis O'Brien's free kick to fire Wrexham into the lead.
And Wrexham soon doubled their advantage as Wednesday emergency goalkeeper Ethan Horvath parried George Dobson's effort straight into the path of Moore, 33, who converted the rebound.
However Wednesday, showing incredible fighting spirit, started the second half brightly and soon pulled a goal back when Bannan netted for the first time since New Year's Day.
And with Wrexham shell shocked and retreating further and further back, youngster Cadamarteri completed a remarkable comeback for Wednesday, securing a precious first point of the season.