The Stok Cae Ras was a sea of red as supporters from both clubs gave their all knowing so much was at stake.
However, the home faithful were silenced in the fourth minute as Callum Brittain’s cross was turned into the net by Conway from close range.
Only Watford have claimed more points from losing positions than Wrexham in the Championship this season, and the Red Dragons responded well to that early setback.
They made it 1-1 before the half-hour mark in stunning style as, after Smith was fouled, Windass guided his free-kick beyond Sol Brynn from around 25 yards out.
It got even better before the break as Smith darted in front of Boro captain Dael Fry to head Issa Kabore’s cross into the net.
But home delight swiftly turned to concern as Strelec turned Matt Targett’s cross beyond Danny Ward just two minutes after Wrexham had taken the lead.
The positive and negative outcomes of results elsewhere continued to filter through to the 10,716-strong crowd in north Wales.
Leo Castledine and Luke Ayling both went close to restoring the away side’s lead before Wrexham – who knew they needed to find a late third goal – pushed for a winner.
Substitute Nathan Broadhead broke free before teeing up Windass four minutes from time, although the forward drilled over from the edge of the box – with Smith then having a shot blocked.
And after failing to win, Wrexham’s agony was compounded when confirmation of Hull’s victory against Norwich filtered through as their campaign came to a heartbreaking end.
As for Boro, their attention turns to the play-offs, with Kim Hellberg’s side hosting Southampton at the Riverside Stadium in the semi-final first leg on Saturday, 9 May.
The return leg at St Mary’s Stadium will take place three days later.
