Boss Derek McInnes is confident Aberdeen can end a 14-year league drought at Parkhead to secure a Premiership runners-up climax.
The Dons’ battle to finish second will go to the last game of the season at Celtic following a 1-1 home draw with Rangers.
Aberdeen sit in second spot with a one-point advantage over the Ibrox club and are four ahead of Hibs, who play tonight.
The Dons have failed to earn a point in 25 games at Parkhead since a win in October 2004.
McInnes has called for “big hearts” to end that hoodoo in the all-or-nothing season closer in Glasgow.
McInnes said: “We will go there (Parkhead) with big hearts confident we can get a result. We had to show more than ever that we could lay a glove on Rangers and we did that.
“For long spells we were very good and we got something from the game.
“We will now have to do something similar on Sunday as we have not managed to get anything from Celtic either this season.
“On Sunday we will have to bring a level of performance that allows us to get something to have a fighting chance of second.”
Aberdeen are sweating on the fitness of midfielder Kenny McLean with a calf injury for the trip to Parkhead.
Defender Scott McKenna is suspended and on-loan attacker Ryan Christie is out as he cannot face parent club Celtic.
The Dons had lost all three previous Premiership games to Rangers this season but were on course for a win that would have confirmed European qualification.
They led at half-time through a McLean penalty but Rangers equalised through Ross McCrorie.
McInnes said: “I’m gutted for my players as they put so much into it and should have been getting all the plaudits under the sun for that first hour performance.
“I was absolutely delighted with the performance of my team, in the first half especially.
“We were fantastic and knocked Rangers out of their stride.
“We played with thought, energy and we deservedly got our goal.
“We were very good and Rangers were losing their shape and discipline a little and half-time came at a good time for them.
“In that first half we could not have been any better as we were full of running, confidence and attitude.
“Unfortunately, due to a combination of us maybe lacking a bit of energy and Rangers stepping it up a bit, we only get a point.
“But we will take the point as it might be a very important one.
“We are still ahead of the other two so they still have their points to go and earn.”
Aberdeen went ahead through a penalty awarded when Alfredo Morelos brought down McLean.
Rangers’ interim boss Jimmy Nicholl insisted referee Steven McLean got the decision wrong.
McInnes said: “We deservedly went in front as it was a clear penalty.
“Morelos bundled into Kenny.
“We were unlucky not to add to that and half-time came at the wrong time.”
Scotland international McLean was playing for the last time at Pittodrie as he will return to Norwich City at the end of the season.
He netted the penalty and hit the bar with a superb 30-yard drive.
McInnes revealed McLean sustained a calf injury in the match and could be a doubt for Parkhead.
He said: “Kenny was feeling his calf but he was having such a terrific game we didn’t want to lose him in there.
“Hopefully the calf will settle and Kenny will be okay but we will need to see how he is.
“We are already without McKenna and Christie for Sunday.”
Winger Gary Mackay-Steven was initially ruled out for the Rangers game with an ankle injury but passed a late fitness test.
“Gary Mackay-Steven was a real bonus on the morning of the game,” said McInnes.
“He had responded to some treatment and wanted to give it a go.
“But due to the lack of training the last few weeks, because of the injury, he never carried the same threat in the last 20 minutes.”
Aberdeen’s other rivals for second spot Hibs will tonight face Edinburgh rivals Hearts at Tynecastle.
Defeat for Hibs will confirm Aberdeen’s European qualification.
McInnes said: “Me and my family will sit and watch that (game), hoping Hearts can get a result.”