Chelsea required penalties to overcome a stubborn Norwich City in their FA Cup replay and set up a four-round encounter with Newcastle.
After an underwhelming first half, Batshuayi made a clever run to the near-post and was on hand to poke home beyond Canaries goalkeeper Angus Gunn 10 minutes after the restart.
Antonio Conte's men were on the brink of reaching the fourth round but in the last second of second-half stoppage-time, Jamal Lewis gone on the end of Timm Klose's cross to head home to take the tie to extra-time.
Pedro and Alvaro Morata both picked up first yellow cards for simulation and they then received their marching orders in the second period of extra time.