The 27-year-old put on a dazzling display as he emerged victorious in just over an hour to claim his place in the third round in style.
Medvedev converted both break points as he wrapped up a one-sided opening set in 32 minutes, hitting nine winners along the way, and although he was spared the humiliation of a bagel, Carballes Baena was outclassed throughout.
It was more of the same in the second set as the Russian broke his opponent immediately.
The fourth seed had the firepower and finesse to match, and his Spanish opponent simply couldn’t deal with his thunderous serve and huge forehand.
He conceded just three games on the night as he claimed his 25th win of the year, setting up a third round tie with Alex Molcan of Slovakia.
“After my match with Carlos I thought I needed to use that shot more,” Medvedev joked about the drop shot.
“I’ve always liked drop shots, but it’s not a weapon in my game that I’m going to use 50 times a match. You need to have confidence in the shot and today it worked pretty well.”
Later on, home favourite Frances Tiafoe battled past Japan’s Yosuke Watanuki in what he described as a “brutal” encounter to reach the third round.
Highlights: Tiafoe battles past Watanuki of Japan at Miami Open
The American, who required six match points to eventually secure the victory, somehow withstood a stunning 55 winners from his opponent in the course of the match.
“It was brutal tonight, just one of those nights you try to get over the line,” Tiafoe said.
“I was a little frustrated as I had never seen him play and he played very well and was hitting incredibly from the baseline.
“He was playing lights out and I was on the back foot a lot. He played a hell of a match tonight, so give respect where respect is due.
“He was so red hot but I was hoping his level might drop in glimpses and I did a good job of taking advantage when it did.”
British 11th seed Cameron Norrie suffered a shock 6-3 6-2 defeat to Gregorie Barrere, while Tiafoe’s countryman Ben Shelton also lost out in surprising fashion to Adrian Mannarino 6-4 3-6 6-1 as another Frenchman won through.
Highlights: Norrie and Evans crash out at Miami Open in second round
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