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Mayweather dominated Paul who fatigued and tired near the end of their eight-round clash.
But 'Money' failed to stop the YouTube star during their bout in Miami.
Mayweather showed off his class in the opening exchanges, landing a pair of clean left-hooks and a body shot with Paul delivering a wild flurry at the end of the first round - but failing to land a significant blow.
Paul, though, caught Mayweather with a right-hand in the second round.
The 44-year-old upped the ante in the third round, increasing his aggression as he connected with some very hard left-hooks.
He continued his onslaught in round four, tagging 'The Maverick' who took more punishment in round five.
Paul visibly tired in the latter rounds as the action slowed down, with clinches between the two fighters the story of the final few rounds.
With no judges scoring the contest, Mayweather and Paul battled to a draw.
SHEESH :flushed: #MayweatherPaul pic.twitter.com/Xi7DvJbBcD
- SHOWTIME Boxing (@ShowtimeBoxing) June 7, 2021
Speaking after their exhibition, the former pound-for-pound king called the 26-year-old "tough" and said "he's better than I thought he was... I'm surprised by tonight. Good little work."
Paul said: "Sh*t man, I don't want anyone to tell me anything is impossible ever again.
"The fact that I'm in here with one of the greatest boxers of all time... this is one of the greatest moments of my life.
"It's an honor to grace the ring with him. This is the coolest thing ever. He's tough to hit!"
Asked what's next, he teased: "Floyd Mayweather-Logan Paul 2?"
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