The Millers led through a first-half goal from Michael Smith but were under a lot of pressure from the Owls even before the striker was sent off and Warne's opposite number Darren Moore started piling attacking substitutes from the bench.
Matthew Olosunde's 83rd-minute own goal levelled the scores but it was substitute Freddie Ladapo who curled a shot in from 20 yards as the Millers counter-attacked right at the end of stoppage time.
“I'm really pleased,” said Warne, who was without a number of key players through injury and had captain Richard Wood in self-isolation. “It's on the back of a bad run but our performances haven't been too bad whereas tonight we got two worldies and to score that late on was a bit Disney for me.
“It was a bit of a scratch team and it was a bit of a character game and we we dug deep. I've never seen the dressing room happier. It's a 10-mile walk back to our dressing room and it was the nicest walk we've had.
“I'm really pleased for the lads to perform at that level and physically we ask a lot of them. Fair play to them.”
The result puts Rotherham three points from safety with two games in hand but Warne conceded that under the circumstances he would have settled for the 1-1 draw that would have ended his side's five-match losing streak.
“At 1-0 when we went down to 10 men I thought it was going to be a long time but it was quite enthralling for a neutral and the time wnent quick.
“When the six minutes were up I would have taken a point because they were in the ascendancy and it seemed like they had 12 strikers on the pitch and if I'm honest I wanted the ref to blow the whistle but Freddie broke and fair play to him that was some bravery and ability to do what he did. As soon as he hit it I thought, 'That's got a chance.'
“My assistant Rich (Barker) is pretty straight to my comedy cop and I've never seen him so happy so it must have been a good day.”
Warne said he did not get a clear view of Smith's straight red card for a challenge with Julian Borner, which some felt was harsh.
Support The Yorkshire Post and become a subscriber today. Your subscription will help us to continue to bring quality news to the people of Yorkshire. In return, you'll see fewer ads on site, get free access to our app and receive exclusive members-only offers. Click HERE to subscribe.