Classy Alcaraz toughs it out to reach Wimbledon last 16 over Jarry
The Spanish top seed, seen as the man most likely to end Novak Djokovic's long reign at the All England Club, was off-colour but still won 6-3, 6-7 (6/8), 6-3, 7-5.
A single break in the first set was enough for Alcaraz to edge ahead but he faltered in the second, slipping 4-1 behind.
The US Open champion clawed his way back, forcing a tie-break, but that went the way of his Chilean opponent, seeded 25th.
Alcaraz regrouped and took the third set 6-3 but the errors crept in again and he found himself in trouble at 3-0 down in the fourth.
The 20-year-old survived two break points in the following game and broke back when Jarry went long with a forehand.
He conjured a searing backhand return to break again in the 11th game and served out for the win.
"I'm really happy with the level that I played to get through this really tough match," said Alcaraz.
He added: "It was really, really close. He has great shots... I would say the key is to believe all the time and stay focused."
Alcaraz was playing his second match in two days after heavy rain earlier in the week caused a scheduling headache for tournament chiefs.
He is attempting to become the third-youngest player in the Open Era to win the Wimbledon title after Boris Becker and Bjorn Borg.