The court suspended the execution of the two men, Mukesh Singh and Pawan Gupta, while an appeal is heard and asked authorities to "communicate the order to prison authorities".
The court held an emergency weekend sitting to hear the motion for the stay. It was not immediately known when the executions had been due to be carried out.
Gupta and Singh appealed to the Supreme Court after the High Court on Thursday upheld the death penalty handed to the four men convicted of the gang rape last September.
The Delhi High Court upheld the four men's sentences in the death of the 23-year-old physiotherapy student, saying the case fell in the "rarest of rare category" under which India carries out executions.
The Supreme Court was told that the other two men convicted of the crime, Vinay Sharma and Akshay Thakur, had not approached the top court to appeal the High Court ruling.
A fifth suspect had been discovered dead in his jail, in what authorities said was a suspected suicide.
The sixth member of the group, a juvenile at the time of the crime, is serving a three-year sentence.