Boss Derek McInnes hailed Aberdeen for an “outstanding” fight back that strengthened the bid to finish third.
Trailing 1-0 the Dons were staring down the barrel of a damaging fifth successive home Premiership defeat.
Hibs were reduced to 10 men with the 55th minute dismissal of Steven Whittaker.
McInnes was delighted with the way his side made the most of that extra man to triumph 3-1.
Having secured a first home league win since December 26 McInnes has challenged his squad to use the comeback as a catalyst to delivering European qualification for a seventh straight season.
The win opened up the chance for the Reds to overtake Well on Friday when the teams meet in a third-placed showdown at Fir Park.
McInnes said: “I thought everybody to a man were outstanding in the second half.
“The players have to deliver the performance and they did it brilliantly.
“We played with assurance, confidence and intelligence when they went down to 10 men.
“It is so important that we finish third at the end of the season.
“It is an important game and clubs like Aberdeen should be playing meaningful games at this stage in the season.
“I am not really interested in how the table looks just now.
“We have got ourselves in a situation through inconsistency, particularly either side of the new year.
“Now what we have to do is that consistency of performance we have been seeing away from home and that consistency of results of late.
“The players deserve so much credit in winning a really meaningful, important game.
“As long as we keeping winning and picking up results the next game will become just as important.
“Motherwell next week will be just as important.”
Aberdeen were trailing to a Christian Doidge goal and the disastrous home league form was in danger of continuing.
However, the Reds were ruthless in putting 10-man Hibs to the sword following the dismissal of Whittaker in the 55th minute.
An own goal from Adam Jackson drew them level before goals from Andy Considine and Curtis Main secured the win.
McInnes was frustrated that referee John Beaton did not award a penalty when the Dons were 1-0 down when Lewis Ferguson was brought down by Greg Docherty.
He said: “We were probably disappointed that we did not get a couple of big decisions in the first half.
“Considine was grabbed round the neck and dragged down.
“As a consequence he goes to ground and whether the ball is in his area or not is neither here nor there.
“The Ferguson one is the one I am most disappointed and angry with.
“Ferguson was just trying to work an angle to get his shot away.
“He was brought down and I was surprised that wasn’t given.
“There was a bit of a grievance again at half-time.
“We have shown in the past how good we can be coming from behind but we had it all to do.”
McInnes accepts the second yellow awarded to Whittaker after 55 minutes was a turning point in the game.
Whittaker was booked for a second time for a clumsy challenge on midfielder Ferguson. However, McInnes insists the Reds were not calling for Whittaker to be dismissed.
McInnes said: “It was a huge moment when Whittaker was sent off.
“We are not looking to get Whittaker sent off.
“He stands over the ball to stop us and kicks it away.
“We had Dean Campbell sent off here two weeks ago with something similar.
“Dean was on a yellow card and did the same, with a different referee.
“John Beaton dealt with that situation the way referees should deal with it.
“We don’t want people sent off for that. However, Whittaker’s tackle got him sent off and I thought from there on in we played with determination.
“We got the ball into wider areas but the intelligence of the team was what pleased me most.”
Aberdeen’s defence were weakened with confirmation last week Scotland international centre-back Scott McKenna is out for the season with a hamstring tear.
The Dons are closing in on a move to sign Tommie Hoban on a short-term deal until the end of the season.
Republic of Ireland international Hoban trained at Cormack Park with the Dons on Thursday and Friday.
Hoban suffered anterior cruciate ligament damage that required surgery while on loan at Aberdeen last February.
Hoban, a free agent having been released by Watford, must prove his fitness to earn a Dons deal.
He returned to his home in England at the weekend as his wife is set to give birth.
Hoban was set to return to Aberdeen today to continue his bid to win a deal.
McInnes said: “Tommie has done well the last couple of days but his wife is set to give birth.
“He went back down on Friday night and hopefully it all went well.
“Tommie will be back up with us (today).”