The Spaniard returned to action after nearly five months out with a straightforward first-round victory over Roman Safiullin on Monday, but found himself on the back foot in his first evening session match this year.
World No.72 Faria broke for a 4-3 lead and relied on his powerful serve to comfortably claim the first set, before piling the pressure on an error-prone Alcaraz at the beginning of the second to earn two more opportunities to break.
"It was a tough match. I was feeling great, but I was in a rush and I didn't take time and it cost me a break (in the first set)," Alcaraz said.
"Against someone like Jaime, who serves at 140-141 miles per hour every time, you have to try and be focused and calm. I told myself good things are going to happen. I just had to stay there all the time."
The seven-times grand slam champion will now meet meet China's Wu Yibing.
Earlier, Daniil Medvedev overcame an unusual interruption from two birds to fly into the third round as he flattened American wildcard Sebastian Gorzny 6-1 6-3 7-5 at Louis Armstrong Stadium.
The 2021 champion fired off 14 aces in a lopsided affair, where a mid-match avian distraction served up an odd bit of drama.
Medvedev next plays Frenchman Arthur Rinderknech, who beat Spain's Jaume Munar 7-6 (7-4) 6-2 7-5.
"Being on the court, I was happy with my level," the Russian said after the match. "I love this court and I love you guys."
The Russian broke his opponent from the baseline in the opening game and needed only 21 minutes to get through the first set, firing off 10 winners to just two from Gorzny, who was outmatched in only his second major main-draw match.
Medvedev has kept a calm demeanour in New York - in contrast to his dramatic first-round exit last year - but had his patience tested when a pair of birds appeared on the net during a rally midway through the second set, prompting the umpire to replay the point.
"I saw them straight away and thought the point would stop straight away," said Medvedev, who estimated they continued to play for 45 seconds before the umpire intervened.
"The moment I hit the winner we stop and I say why?"
But he got over it pretty quickly and didn't trip like Rafael Jodar, the Spanish 12th seed who was ousted 6-2 6-1 6-1in his maiden US Open campaign in the first round by Chinese lucky loser Bu Yunchaokete.
"I'm a really lucky loser," said Bu, who only got in after Australia's Thanasi Kokkinakis withdrew.
"After I lost in qualifying, I took a day off but I saw a few guys pull out, so I took the decision to come back and tried to do some work in case I could play. Yesterday, they told me I could ... when I heard that, I was super excited."
Ben Shelton survived a tough test from Poland's Hubert Hurkacz 6-3 5-7 7-6 (7-3) 7-5 before reaching the third round, relying on the deafening cheers of the partisan American crowd to power him through.
Alex Michelsen pulled off an upset by ousting another American Brandon Nakashima, the No.16 seed, 6-3 6-4 6-4.
No.11 Frances Tiafoe beat Japanese qualifier Rei Sakamoto in straight sets, while Argentina's Mariano Navone backed up his upset of Novak Djokovic by beating Matteo Berrettini 3-6 6-3 6-4 7-6 (7-4).
Peruvian Ignacio Buse beat Marcos Giron 3-6 6-3 6-3 6-7 (8-6) 6-1, while Stefanos Tsitsipas beat South African Lloyd Harris 6-7 (7-1) 6-3 7-6 (7-4) 6-4.
