Djokovic battled to find his form as he lost the first set to Tsitsipas 6-4. The Greek star was playing the big points much better than the Serb, who made some uncharacteristic errors in a difficult first set.
But any hopes of a second set fightback were replaced with more concern as Djokovic was broken in the third game of the second set to put him in big trouble as the rain came down in Italy.
Shortly after losing his serve and going 2-1 down in the second set, the play was suspended due to the worsening conditions on court, with Djokovic's stern expression hiding what was likely relief at some respite and the chance to reset before play resumes.
The match was first halted for 3 hours 30 minutes with the fifth seed leading 4-3 before heavy rain hit the Italian capital.
Play will resume tomorrow.