The defending champion needed to dip into his armoury of explosive winners to lastly see off the British quantity two inside Arthur Ashe Stadium.
The final time Evans performed the top-ranked participant he rose to the event, beating Novak Djokovic in Monte Carlo three years in the past.
And the twenty sixth seed introduced the perfect out of the 20-year-old Wimbledon champion earlier than succumbing 6-2 6-3 4-6 6-3.
Alcaraz dominated the primary set, always pushing his opponent to the again of the court docket and hitting 14 winners to Evans' 4.
But he confirmed he isn't infallible at the beginning of the second after a double-fault gave Evans, who was starting to relish the problem, a break level which he transformed with an outstanding backhand down the road.
Alcaraz shortly retrieved the break and a annoyed Evans was given a code violation after slicing the ball into the gang after netting a volley at 15-30 up on the Spaniard's serve.
Evans was enjoying nicely, however Alcaraz merely raised his degree and introduced up set level with a blistering forehand down the road which introduced gasps from the spectators.
Evans saved that one, however might do nothing with the following after an beautiful lob and easy volley put Alcaraz two units up.
Never one to surrender and not using a combat, Evans promptly performed probably the greatest units of his profession.
He broke for 4-3 and, serving for the set, pressured Alcaraz into a few of the most outrageous clutch winners.
The pair, who performed golf collectively at Wimbledon, continuously exchanged realizing appears to be like and grins, such was the standard of the cat-and-mouse tennis on present.
It took Evans, 33, 5 set factors to make the breakthrough, prompting a all of the sudden exasperated Alcaraz to slam his racket down in frustration.
But Alcaraz turned the match again in his favour with one other gorgeous shot on break level. On the run and at full stretch, he unleashed a forehand down the road which clipped the baseline and left Evans stood, arms on hips, in sheer disbelief.
Two aces, one other sensational lob onto the baseline and a 61st winner of the match completed Evans off, however Alcaraz knew he had been in a contest.
"He's a tricky opponent, great slices, good touch and it's my game as well so it was a pretty good match," stated Alcaraz.
"We made great points, great shots, a lot of different situations, so I'm really happy to get through
"We performed some nice factors that made us smile, Dan as nicely. It's nice to see Dan and I on a tennis court docket, we tried to entertain and make the match enjoyable."
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