Wednesday can now look forward to Championship football next season which had seemed wildly out of reach when they trailed Peterborough 4-0 after the first leg of their semi-final before producing the greatest comeback in English Football League play-off history.
In front of 44,000 Wednesday fans crammed into Wembley, Windass emulated his father Dean, whose winning goal for Hull City in the 2008 Championship play-off final helped them win promotion to the Premier League.
In an action-packed period of extra time, Wednesday's Michael Smith and Barry Bannan had efforts saved before Windass sent a diving header past goalkeeper Harry Isted in the 123rd minute to spark rapturous celebrations.
"There's no words, there's no words. Wow," Dean Windass told BBC Radio Sheffield. "I knew he'd score, this morning when I woke up at 5.30 I was nervous and even with his head as well - I can't believe he's headed it.
"I'm so proud for him. When I scored here I thought my life would change. I've got two boys but this boy - it's unbelievable."
Wednesday, who narrowly missed automatic promotion to the Championship from the third tier in the regular season, fell to a thumping defeat in the first leg of their playoff semi-final against Peterborough to leave their promotion hopes in tatters.
But they stunned Peterborough 5-1 at Hillsborough in the return leg before prevailing on penalties.
"I've played for a couple of big clubs but look at this, it's unbelievable," Josh Windass told Sky Sports.
"We've been good on the pitch this year. The club's got a lot of work to do to catch up with the other clubs off the pitch, but hopefully we can do that and start being the giant club that we are."
