Costa's recent dry spell sees him make way for Belgian Batshuayi, although in-form Hazard is also among the substitutes for Conte.
Ake has played just twice - both appearances coming in this competition - since he saw his loan move to Bournemouth end early in January.
Despite his lack of game time for the Blues in recent months, Cahill's omission from Conte's squad due to gastroenteritis has resulted in the Chelsea boss putting his faith in Ake over Kurt Zouma, who started in the 2-0 loss to Manchester United last Sunday.
Meanwhile, goalkeeper Thibaut Courtois is in Chelsea's starting XI after he recovered from an ankle injury, which kept him sidelined for the trip to Old Trafford.
Marcos Alonso also makes the cut following a bout of illness that meant he missed the game against United, with Conte picking a strong XI for the semi-final against Spurs.
Chelsea starting XI: Courtois, Azpilicueta (c), David Luiz, Ake; Moses, Kante, Matic, Alonso; Willian, Batshuayi, Pedro
Chelsea subs: Begovic, Zouma, Terry, Chalobah, Fabregas, Hazard, Diego Costa