Battery Operating ESP8266 Board

I am working on a PCB board design which is battery optimized. ESP will be programmed in Arduino.
ESP8266 has very good power management scheme. I will include a DS3231 with a super cap for Vbat.
Power output of the board will be connected to a FET. Therefore external peripherals can be shot down.

My question is about the electrical circuity around DS3231. I want to shot down its power when ESP goes sleep. Vbat will be connected. How can I enable DS3231 interrupts while consuming minimum power. When Vcc connected it draws 200uA. That's more than ESP sleep. Therefore I would like to shot it down just to enable interrupts. I also read in Internet DS3231 can get power from I2C pins, I don't want that.

Summary of my question: Enable DS3231 interrupts on ESP8266 while consuming minimum power.
All Circuit designs are welcome.