James Vaughan's 82nd-minute equaliser appeared to have consigned Barnsley to League One, but Crystal Palace's 89th-minute winner against relegation rivals Peterborough meant both Yorkshire sides stayed up.
Huddersfield twice hit back from behind to clinch a 2-2 draw and the point they needed to guarantee Championship football next season.
Jermaine Beckford cancelled out Chris O'Grady's first-half opener and Vaughan silenced the visiting hordes after substitute Jason Scotland had headed Barnsley into a 75th-minute lead.
Once news of Palace's late winner had filtered through, it triggered bizarre scenes on the pitch, where both sets of players swapped handshakes and appeared to agree to play out the final few minutes without further incident to ensure both sides avoided the drop.
When asked how he would celebrate, Flitcroft said: "I'm not sure. I don't know where I'm at. I'll go up to my dad's grave tonight and probably spend an hour up there with dad.
"After the greatest achievements I've done in my life, I've spent them at a grave in Bolton.
"There's a lot of emotions. I just wish dad could have been here to witness that."
Barnsley were clear favourites for relegation when Flitcroft was named as a surprise replacement for the sacked Keith Hill in January, but an impressive run of form over the second half of the season has rescued the club.
"Mission Impossible achieved," Flitcroft said. "We've not been lucky in the last minute, we designed that since day one when we took over. We've beaten some incredible football teams and Mission Impossible can only be achieved by special people."
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- James Vaughan