The 34-year-old Goffin beat Alcaraz three years ago in Astana in their last meeting and sensing the Spaniard was far from his best in the opening set, he went on the attack.
The 55th-ranked Goffin, whose world ranking reached No.7 in 2017, struck some glorious winners while Alcaraz was struggling with unforced errors.
The slightly built Goffin was up by a break in all three sets but having let Alcaraz recover in the first he showed poise and calm to stay on top.
"When I came out earlier... just to warm up on the court, I felt 'I'm moving well. I'm feeling quite relaxed. I'm hitting the ball really well' and so I hoped it would be the same during the match.
"I started the match well. I had the break in the first and he started to play really well at the end of the first.
"It's that kind of night that I will remember for sure - against Carlos and in a stadium like that. And the night that gave me a lot of confidence to continue," he added.
Six-time champion Novak Djokovic made his long-awaited Miami Open return on Friday and defeated Australian Rinky Hijikata 6-0 7-6(1) to reach the third round.
It marked Djokovic's Miami return for the first time since 2019 and the Serbian fourth seed's victory was his 410th ATP Masters 1000 level match win, tying him with Rafael Nadal for the most of all time.
"I was playing really well, I mean on a very high level from the beginning, I knew exactly what I wanted to do tactically," Djokovic said during his on-court interview.
"Obviously it's just the first match but the way I felt on the court and the way I played is really encouraging."
It was all one-way traffic in the opening set as Djokovic showcased his superior shotmaking from the baseline along with a lethal service game to make a perfect start and needed just 27 minutes to wrap up the opening set.
But Hijikata refused to back down and his confidence grew during a tightly-contested second set where neither player could manage a break but Djokovic took over in the tiebreak where he won the final six points.
Russian seventh seed Daniil Medvedev, the 2023 Miami champion who arrived this year fresh off a run to the Indian Wells semi-finals, crashed out at the first hurdle as he fell 6-2 6-3 to Spaniard Jaume Munar.
Former Miami finalists Casper Ruud and Grigor Dimitrov both advanced while Australian Kyrgios, who this week earned his first win since October 2022, fell 7-6(3) 6-0 to Karen Khachanov.
On the women's side, Andreeva, making her Miami Open debut fresh off winning the first leg of the Sunshine Double at Indian Wells, was a 6-0, 6-2 winner over Veronika Kudermetova and will next face Doha champion Amanda Anisimova.
Swiatek beat Garcia in straight sets at the same stage in Indian Wells where the Pole's title defence ended last week in the semi-finals but faced a much more determined opponent this time around.
Swiatek powered through the first two games of the match without dropping a point and then consolidated another service break for a 4-0 lead before leaning on her serve to secure the first set in 29 minutes.
But the Pole faced much more resistance during a back-and-forth second set as she overturned a 3-1 deficit and then saved a set point while serving at 5-4 down as she closed out the match by winning the last three games.
Up next for Swiatek will be Belgian Elise Mertens, who advanced with a 6-4, 6-1 win over American Peyton Stearns.
Australian Open champion Madison Keys advanced with a 6-3, 6-3 win over Armenia's Elina Avanesyan to set up a third round clash with Filipino wildcard Alexandra Eala, who beat Latvian 25th seed Jelena Ostapenko 7-6(2), 7-5.
Former US Open champion Emma Raducanu also advanced with a 7-6(6), 2–6, 7–6(3) win over Emma Navarro. Among the other women advancing were Spanish 10th seed Paula Badosa and Czech 15th seed Karolina Muchova.