0744 GMT July 19, 2018
The German Wunderkid, 21, looked to be on the brink of another disappointing early exit from a Grand Slam, with 26th seed Dzumhur serving for the match at 5-4 in the fourth set, Reuters reported.
But Zverev held his nerve to force a tiebreak, which he won comfortably.
Matching Zverev for power and stamina and showing a fine touch, with multiple winning drop shots, Dzumhur took the match to his bigger opponent, pushing the German to his second five-set encounter in a row.
In their only previous meeting, last year in Shenzen, Dzumhur won in straight sets and he showed confidence throughout on Friday, until the closing stages.
Zverev's win, which secures his spot in the fourth round in Paris, was his first against a top 50 player in a Grand Slam.
Grigor Dimitrov’s French Open hopes bit the dust as the fourth seed was outplayed by Spanish veteran Fernando Verdasco in the third round on Friday, the Bulgarian losing 7-6(4), 6-2, 6-4.
Dimitrov was pushed to five sets by American Jared Donaldson in the previous round and once he failed to convert four set points in the 12th game of the opener against Verdasco and lost the ensuing tiebreak, he looked flat.
The aggressive left-handed Spaniard broke twice in the second set and although he allowed Dimitrov back from 4-2 in the third, he broke again to claim his third career win against the 27-year-old.
Verdasco has now reached the last 16 in Paris for the seventh time and will hope to finally break through that barrier having fallen at that stage on six occasions.