The world No 2 produced a determined response after dropping two sets, but must resume his first round match with Stepanek on Tuesday after the players were forced off by the gloomy conditions at Roland Garros.
Stepanek, the oldest player in the draw at the age of 37, produced a sprightly start to the match and frustrated Murray with a string of drop shots.
Murray was struggling to contain his irritation, appearing to direct his angry mutterings towards his coaching team, and fumbled a forehand into the net to concede the opening set.
His mood grew as murky as the conditions on court when he allowed Stepanek to instantly break back in the second set and the Czech confidently broke again on the way to his two-set lead.
The Scot did not drop a game in the third set
The threat of an early exit was met by a furious response from Murray, who repeatedly bellowed a 'let's go' mantra while racing through the third set without dropping a game.
Sensing that Murray was on the march, Stepanek wanted the match to be halted at that point, but the umpire ignored his protests and Murray broke again to take command of the fourth set.
But both players signalled that the match should be postponed, with the light fading fast, and Murray will be hoping to continue his impressive recovery when play restarts.
Kyle Edmund has reached the next stage at Roland Garros
But Kyle Edmund is safely through to the second round for the second successive year after a four-set win over qualifier Nikoloz Basilashvili.
The 21-year-old Yorkshireman battled to a a 7-6 (7/4) 6-7 (9/7) 7-5 6-1 victory that lasted two hours and 47 minutes.
