The combative Argentine, who helped Atletico to the league and King's Cup double as a player in 1996, has transformed the Spanish capital's second club since taking over from Gregorio Manzano in December 2011.
The Europa League champions are three points behind leaders Barcelona after 13 matches and, unbelievably for many of their long-suffering supporters, eight ahead of stuttering Real, who slipped to a third defeat of the campaign at Real Betis last weekend that left their title defence in serious peril.
Simeone, a tough-tackling midfielder sometimes described as "playing with a knife between his teeth", has given his players added steel and in Colombia striker Radamel Falcao they have a genuine goal scorer who has attracted the attention of the sport's big spenders.
Turkey playmaker Arda Turan is also having an impressive season, linking well with Falcao and scoring goals of his own, while the defensive line has a solidity that has been sorely lacking in recent years.
"I think bringing in Simeone has been a success for Atletico," Real captain Iker Casillas said on Wednesday.
"He has given them a new spirit and no one has gifted him anything," added the Spain goalkeeper.
"Falcao is a great player. He was a very successful signing and is a very complete, natural finisher."
Claudio Ranieri was the last Atletico coach to savour victory over Real, when former Netherlands striker Jimmy Floyd Hasselbaink scored twice in a 3-1 away triumph in 1999.
A win or even a draw on Saturday could spell the end of Real's hopes of a second straight La Liga title and Casillas is well aware of what is at stake.
"It is a different match from previous seasons," he said.
"They are coming to the Santiago Bernabeu with a very strong team and after a win in a very tough match against Sevilla, who beat us.
"We hoped that there would be less of distance between us, but hopefully at the end of the match that advantage will be cut to five points. Any aim other than winning is no good for us."
Real's Portuguese coach Jose Mourinho was whistled by some sections of the Bernabeu crowd during Tuesday's Cup victory and their reaction on Saturday will be closely watched.
The team's erratic form has prompted speculation the former Inter Milan and Chelsea manager will not last the season, with almost 70 percent of voters in an internet survey conducted by As sports daily saying they believed he would be gone by May.
"The club is the club and is in charge and I'm just an employee trying to do their best," Mourinho told a news conference previewing the cup match on Monday.
"The club has to decide if it is happy with the path we're on and we'll get to the end of season calmly," he added.
"It is possible that at the end of the season the club will not be happy with my work and that things have to change."
WELL RESTED
Unbeaten Barca, meanwhile, will seek a 13th win in 14 games and look to increase
