Thiam, his right eye swollen, quit with 12 seconds left in the third round before a heavily pro-Trinidad crowd at American Airlines Arena.
Trinidad improved to 38-0 with his 31st knockout, while Thiam dropped to 33-2.
"It was a hard fight. It feels great to win for my country," said Trinidad, from Puerto Rico.
Trinidad landed 55 percent (96 of 175) of his punches, while Thiam landed 25 percent (34 of 136). Trinidad landed 72 of 118 power shots.
Trinidad stung the French challenger with a left hook and an uppercut in the first round, sending Thiam to the ropes. Trinidad unleashed a seven-punch combination as Thiam staggered away.
By the end of the round, Thiam's right eye was closed and Trinidad made the overmatched No. 1 contender look slow.
Thiam attacked Trinidad in the second as both men went toe to toe. Thiam connected with a couple of left hooks in the round but exited his corner to start the third nearly blind from the cut.
Thiam, the European 154-pound champion, struggled to leave the ring after the fight but walked to the locker room without help.
It was a mandatory defense for Trinidad, who completed his first defense of the WBA 154-pound belt.
Fernando Vargas, the IBF 154-pound champion, is likely next for Trinidad. Vargas faces mandatory challenger Ross Thompson on Aug. 26. A possible Trinidad-Vargas fight is earmarked for Dec. 2.
Trinidad reportedly earned $2.5 million, while Thiam made $200,000.
The full upper bowl of the arena, where tickets sold for $15, $30, and $45, was filled with fans waving Puerto Rican flags and produced a deafening roar when the island's hero was introduced.
Trinidad's team then unfurled a flag on stage as he strolled into the ring led by trainer and father Felix Sr.
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