The judges each scored the fight 48-47 in favour of Bisping, who now has a record of 29-7.
He is now ranked seventh in the division, while Silva is fifth but winless since October 2012.
“I worship this guy,” said Bisping of Silva post-fight. “This guy is the greatest martial artist of all-time. This has been a lifelong quest. Anderson, thank you.”
“The mission was given and I thought the mission was completed, but I guess not,” said the 40-year-old Silva, a future Hall of Famer who reigned over the division from 2006 to 2013.