The lively Kalinic shot wide under pressure from Ferreira shortly before his ninth-minute opener.
Rovers levelled when Kalinic attempted to head Emerton's deflected cross at the near post.
They reportedly fell out when Mr Kalinic had an affair with Mr Simovic's wife.
ECONOMIST: Serbian and Croatian police are starting to work together
Kalinic then forced a good save from Hilario but Chelsea survived to take the match into extra-time.
Nikola Kalinic was sent off for the home side before Fabian Frei followed him down the tunnel.
Ciaran Clark nodded Villa ahead but Rovers were quickly level as Nikola Kalinic bundled home from close range.
Blackburn's Nikola Kalinic was unlucky to have a late strike ruled offside as Michael Owen missed from close range.
Nikola Kalinic put Rovers ahead from six yards before a header from substitute Didier Drogba and Salomon Kalou's finish sent Chelsea in front.
Blackburn threatened sporadically on the counter-attack - Benni McCarthy and Vince Grella drilled wide before Kalinic tentatively prodded wide when one-on-one with Reina.
Allardyce desperately needed a change in momentum and introduced striker Jason Roberts for Nikola Kalinic - a decision not popular with the local fans.
Rovers briefly rallied and Pires had to hack a Kalinic shot off the line while Friedel pushed a Chris Samba header round his post.
Rovers brought on David Dunn for Brett Emerton at the break and played slightly higher up the pitch in an attempt to support Kalinic.
Benni McCarthy's shot was well saved by Edwin van der Sar and substitute Kalinic fired into the net with the referee's assistant waving for offside.
City had gone behind when a mix-up between keeper Joe Hart and Kolo Toure allowed Nikola Kalinic to steer in a shot from outside the area.
Rovers started with Nikola Kalinic as the lone striker and the Croat, competing against the considerable presence of Rio Ferdinand and Nemanja Vidic, struggled to hold the ball up.
Michel Salgado stormed down the right flank and Kalinic got enough on his cut-back to force the ball over the line despite the best efforts of Villa goalkeeper Brad Friedel.
But on a rare foray forward they had a sight of goal when Kalinic worked some space in the City box only to have his shot blocked by the on-rushing Hart.
It was a well-constructed goal that saw Morten Gamst Pedersen play in Pascal Chimbonda, who in turn drilled the ball low across the face of goal for Kalinic to slot home.
At the other end, Nikola Kalinic, returning from a three-match ban, did his best to give Blackburn an outlet, teeing up Martin Olsson for a long-range drive which Petr Cech saved comfortably.
It's just like old times as Blackburn score twice from set pieces to see off the fragile Baggies, while Nikola Kalinic blights an impressive display with an ugly challenge on Paul Scharner.
Rovers had seen Roque Santa Cruz depart with a suspected hamstring injury shortly before the Villa opener but his replacement, Croatia striker Kalinic, did not take long to make an impact on the game.
City centre-back Kolo Toure left Morten Gamst Pedersen's hopeful punt upfield to Hart but the keeper -- having come 30-yards out of his goal -- missed the ball and Kalinic steered in a left-foot shot.
When Milos Simovic shot (but failed to kill) Sretko Kalinic, it turned out that both belonged to Serbia's notorious Zemun gang, which had taken part in the assassination of Zoran Djindjic, the Serbian prime minister, in 2003.
ECONOMIST: Serbian and Croatian police are starting to work together
They eventually went in front when El Hadji Diouf swung in a cross from the left which was flicked on by Nikola Kalinic and Adam, positioned by the far post, tried to cushion a header back to Gilks and watched agonisingly as it rolled over the line.
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