With the 37-year-old Czech belying his advancing years, the world No 2 was forced to dig deep in an enthralling encounter, before a tame Stepanek backhand went into the net at 30-40 to hand Murray the chance to serve for the match.
The Scot negotiated his way to match point before double faulting. In the end he prevailed as the valiant Stepanek planted a volley into the net to hand a visibly relieved Murray victory in three hours and 41 minutes.
Earlier Murray returned to the court 4-2 up in the fourth, after play was suspended due to bad light on Monday night, and he held firm to take the set 4-2.
The Briton, tipped by many to win the event after beating Novak Djokovic in the Rome Masters last week, looked lacklustre in the opening exchanges and was guilty of too many unforced errors in losing the first two sets 6-3 6-3, but he lifted his game to breeze through the third set 6-0 in 18 minutes before moving a break up at 4-2 clear in the fourth.
Play was suspended after 9pm local time due to bad light on Philippe-Chatrier and will resume at 11.30 am on Tuesday.
Stepanek misses simple smash on set point against Murray
The Czech player, 37, made a brilliant start to the match by breaking Murray n the fourth game and ended up winning the set 6-3 after Murray ditched a forehand into the net.
With only around an hour of daylight left for play, the Scotsman dropped the second set by the same margin with a lot of his errors coming on the forehand side.
But the world number two was a man transformed in the remaining passage of play, and will strongly fancy himself to progress with conditions forecast to be less gloomy around the French capital on Tuesday.