The Spanish teen rocketed to stardom as the youngest man to reach the quarter-final at Flushing Meadows last year and looks on track for another memorable run after making 46 winners to just 10 from his opponent inside Arthur Ashe Stadium.
"I played really, really well," the 19-year-old said in an on-court interview.
"I knew that it was going to be a tough match... I'm really happy with my performance."
The third seed has enjoyed a terrific 2022, winning in Miami and Barcelona before downing a fearsome trio of Rafa Nadal, Novak Djokovic and Alexander Zverev to triumph in Madrid.
A crisis of confidence led to an early exit from Montreal but Alcaraz showed no such issues on Saturday when he recovered from a slow start in the third set.
Up a break in the second game, Brooksby gave the home crowd a thrill when he fell backwards during a 17-shot rally but incredibly recovered to win the point. He added to the crowd's elation when he broke the third seed to love in the next game.
The party would be short-lived, however, as Alcaraz won the next six games in ruthless fashion.
Seventh seed Cameron Norrie meanwhile denied using gamesmanship during his third-round win over Holger Rune.
The British No.1 is continuing to live up to his top-10 ranking and kept 19-year-old Rune at arm's length during a 7-5 6-4 6-1 victory to reach the fourth round for the first time in New York.
Rune, already the highest-ranked Danish man in history at 33 and a French Open quarter-finalist this year, has a reputation as a spiky character and during the second set he protested to the umpire about Norrie catching his ball toss before serving.
Players are allowed 25 seconds between points but the clock stops when the server throws up the ball, meaning catching the toss buys extra time to reset.
Rune implied to the umpire he thought Norrie was deliberately exploiting a loophole in the rules, although he was more diplomatic in the press room later.
"It's a bit annoying. I'm not controlling the rules but I think you can do it a couple of times but doing it 10, 15 times is maybe too much," said the teenager.
The pair had met twice before, with both matches going to a deciding set, but here Rune could offer no real resistance as Norrie eased to victory.
"I thought I played a bit better than I did in the previous match, so that was great. I felt way more comfortable. It was nice to be on Grandstand," Norrie, whose run to the Wimbledon semi-finals was the first time he had gone beyond the third round at a slam, said.
"It was tough playing against Holger. He can come out and play very aggressive and can come forward very well. He's extremely talented, and he's a young up-and-coming player, but it was nice to get through in straight."
With PA.
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