With a 7-5, 6-1, 7-6(6) victory on the Court Philippe Chatrier stage, the 37-year-old French wild card earned his 500th match win, moving to the third round.
The match ended with Hugo Gaston recording an unlikely victory over Alex de Minaur by a score-line of 4-6, 6-2, 6-3, 0-6, 7-6 (10-4).
The Norwegian Ruud came out as the victor after what was a thrilling contest that saw a brilliant tie-break in the very first set.
The Norwegian's defeat came at the hands of Dutch player and eighth seed Botic van de Zandschulp.
Alcaraz is the youngest Miami men's champion in the event's 37-year history, as well as the third-youngest ATP Masters 1000 champion overall.
Zverev did make an outstanding comeback in the second set after losing the first, but his opponent on the day was just too good.
He's a counterpuncher who grinds opponents down with heavy topspin and his strongest shot is a heavy topspin forehand, which he uses to move opponents around the court.
His maiden ATP title win came only a few months ago when he displayed impressive skill and resolve to win the 2021 Stockholm Open.
Harris has three ATP Challenger singles and two Challenger doubles trophies, as well as 13 ITF singles and four ITF doubles titles.
The 23-year-old Norwegian won five ATP titles in 2021 and made it to the semi-finals of a couple as well.