Persistent rain in Melbourne meant the match, which was last on the schedule, did not begin until 10pm local time having been moved to an outside court.
There were a few more brief stops for drizzle, disruption by rowdy spectators and plenty of twists and turns before Norrie finally wrapped up a 6-3 3-6 7-6 (2) 6-3 victory over his unseeded French opponent at 1.28am.
A handful of fans, some wrapped in blankets to keep out the unseasonal chill, stayed to the end as Norrie moved through to a third-round clash with talented young Czech Jiri Lehecka.
The late night meant a tricky few hours for the umpire, who sent three English spectators, beer cans in hand, from the court after abusing Norrie at the end of the first set and also told a fan off for loudly swearing during the fourth.
Lestienne's story is one of persistence, the 30-year-old Frenchman making his main draw debut at a grand slam after falling in qualifying 21 times.
He drove Norrie to distraction with his unconventional use of slice and trick shots, which included an attempted lob played through his legs when down set point in the opener.
The British number one smashed that one away but things became complicated in the second and he looked in real trouble when down 5-2 in the third.
But Norrie, seeded 11, has toughed out so many matches over the past two years and he fought his way back, winning the set on a tie-break, before finally overcoming Lestienne and his own frustration in the fourth.