Coming off a brutal brawl with Ruslan Provodnikov last March that took him two months to recover from, Bradley vowed to avoid a war with Marquez. He used his left jab to keep the Mexican away and boxed from the outside for most of the bout before trading wild punches in the final round.
"He couldn't touch me," Bradley said. "I gave him a boxing lesson."
Marquez was in the fight the entire way but at the age of 40 he seemed less active than in earlier fights. Bradley was the aggressor most of the night and seemed to control the action from the middle rounds on.
"I came to win. I felt that I did win," Marquez said. The judges took it away. You don't have to knock out a guy to win."
The decision loss was the latest in a series of disappointing decisions that went against Marquez. He fought Pacquiao three times, losing twice and getting a draw on narrow decisions before finally knocking him out.
"I've been robbed six times in my career," Marquez said. "I clearly won the fight."
Marquez, like Bradley, passed up a rematch with Pacquiao in favor of this fight. Marquez knocked Pacquiao out in the sixth round last December, but could never find his big punch against Bradley.
Pacquiao will fight in Macau next month against Brandon Rios instead.
Bradley remained unbeaten in 31 fights with the win, his third narrow decision win in a row. Marquez fell to 55-7-1 and may be near the end of a career that has made him one of his country's biggest champions.
Both fighters earned $4 million.