The athletic heavyweight blasted Griggs seconds into the fight with a flying knee that dazed the Strikeforce veteran before using a bodylock to put him on the mat. There, Browne blasted him with a series of left hands before locking in the fight-ending choke.
The finish came at 2:29 of the first round.
Afterward, Browne credited Griggs on his toughess, wondering how he could have stayed upright following the knee, but said he was offering a message to the rest of the division as well.
"I belong here. UFC heavyweights, watch out, baby," he said.
Browne improved to 13-0-1 with the impressive victory. He's 4-0-1 in the UFC. Meanwhile, Griggs suffered his first defeat since 2007, and fell to 11-2. Griggs had been making his UFC debut after moving over from Strikeforce.