He did not return for the second half, and the team announced he was under evaluation for a concussion and was ruled out for the rest of the game.
Moore went 17 of 28 for 282 yards, including a 61-yard scoring pass to Kenny Stills to tie the score at 20 with 3:00 left.
Miami (4-6) saw its last-ditch attempt on a final play with multiple laterals, but a loose ball was recovered in the end zone by Glanton for the clinching touchdown.
It is not known if Moore will start in the Dolphins Week 12 game against the New England Patriots, but he always appears to be ready when his number is called.More news: South Carolina Women's Hoops Teams Turns Down White House Invitation
Cutler, who signed a one-year deal worth $10 million prior to the season after a season-ending injury to Ryan Tannehill, was 6 of 12 for 83 yards with a touchdown and the three picks. Miami forced a field goal chance and the miss by Patrick Murray from 42 yards away kept the Dolphins in the game.
Cutler was tackled on the next-to-last play - a 1-yard run - of the first half by Tampa Bay's Ryan Russell. Miami outgained the Bucs 167-21 in the third quarter, giving up pass plays of 49 and 45 yards, but the Dolphins could only get two field goals to cut the lead to 20-13 entering the fourth quarter.
Maualuga's replacement: The Dolphins had to make a last-minute switch on defense following the arrest early Saturday morning of starting middle linebacker Rey Maualuga.