Paul is a self-proclaimed fan of the retired Silva but was far from star-struck when the pair squared off in the ring.
"I feel like I'm living in a movie," Paul said afterwards. "You couldn't have written this in a story.
"Just being in the ring with him, seeing his heart, his courage, his bravery, that's the champion that I looked up to. He's such an inspiration."
The fight went the full eight rounds with Paul managing to knock the 47-year-old Silva down once only in the final round.
Even though he didn't win by knockout, it was another convincing performance by Paul who received a unanimous decision of 77-74, 78-73, 78-73 to move to a 6-0 boxing record.
Silva was the third MMA fighter Paul has boxed and, in keeping with that tradition, called out Nate Diaz as the person he wants to fight next.
"Everyone wants that fight," Paul said. "Nate, stop fighting people for free, let's do it in the ring."