Motherwell will go into the Dons replay buoyed by a 3-2 win over Ross County that saw the club claim their first home victory in 10 weeks and jump up to third place in SPL table.
With Well having drawn 3-3 at Aberdeen in the league before then being held 1-1 by Craig Brown's men in the Scottish cup, the Fir Park gaffer accepts that there is nothing between the two sides.
But with the Lanarkshire men nursing a large amount of frustration from these two meetings, after late goals on both occasions salvaged an unlikely league point and forced a cup replay, McCall is determined to make it third-time lucky against the men from Pittodrie.
He said: "I don't think you could lay a bet with any certainty on either side ahead of tonight's tie.
"Both in the league and in the cup we have put ourselves in winning positions but they [Aberdeen] have come back strongly to claim a draw.
"So there is a fair amount of frustration that we were unable to put either of these games to bed and that will be a strong motivation for us tonight.
"There is also the importance of a cup run both in financial terms and also for the sheer excitement it generates.
"What is very important for us ahead of the tie is that we have finally got that home win we have been searching for after beating Ross County.
"So we have the ideal springboard into this one and that is huge."
McCall has injury concerns over top scorer Michael Higdon, who took a knock against County, and midfielder Nicky Law, while first pick keeper Darren Randolph is certain to return between the sticks at the expense of Lee Hollis despite his heroics against the Dingwall side.
But the Well boss admits that he is also keen to get the better of Craig Brown, who was his predecessor at Fir Park, as he looks to wipe out the memory of a defeat to the Dons at the quarter-final stage of last season's Scottish Cup that continues to touch a raw nerve with the Steelmen.
McCall said: "We lost out to Aberdeen at Fir Park in the quarter-final stages of last season's cup and that was a game that, shall we say, had an awful lot going on in it.
"Aberdeen went two up in controversial circumstances with their first from a corner that was never correct and I was sent to the stand and unable to get instruction across for the second-half as I would have liked.
"On top of all that, Keith Lasley was sent off and yet we got a goal back with 10 minutes to go and with 10 men we pummelled them.
"Unfortunately, we couldn't get the equaliser. So definitely that is a cup tie and a game that still looms large in my memory and one we would love to avenge.
"The good news is that we are going into the game with all of our big players on top of their form.
"Tonight is a great chance to make the quarter-finals for the third season on the bounce and that's my target."