Cole had entered the game in place of Dwyane Wade, who didn't return after halftime because of back spasms, the Heat said in a tweet. Wade's return was characterized by the team as questionable.
Wade said after that game that his back "just locked up."
"I don't know," Wade said, as quoted in the Miami Herald. "I'm day-to-day at this point."
Cole went up for the basket with Ty Lawson, who was called for a foul, and fell awkwardly face first to the floor. He remained down for several minutes while being tended to by trainers before being helped to his feet and assisted off the floor to the locker room for treatment.
"He went back and after a few minutes he was fine," Miami coach Erik Spoelstra said. "He is just going to have a fat lip tomorrow."
Cole said his mouthpiece prevented damage to his front teeth.
"Just a little cut on my lip and that's it," Cole said, according to the Miami Herald. "My teeth didn't come out. They would have come out if I didn't have my trays in, but they held them together. They're a little loose, but they're good. ... I put a lot of money into these things."
Joel Anthony came in for Cole and made both free throws.
Information from The Associated Press contributed to this report.