It was the third sack of the game for Freeney, and the fourth allowed by Smith who not only looked like a rookie on Sunday, but a bad rookie at that.
The turnover occurred on a second-and-8 play from the Colts 13-yard line after Terrell Buckley had intercepted Peyton Manning on a third-and-7 pass.
Griese faked a handoff to Ricky Williams and barely had a chance to start rolling out to his right before Freeney hit him from behind to cause the fumble.
The Dolphins had cut the Indy lead to 23-17 on their previous possession when Olindo Mare hit a 23-yard field goal after the Dolphins failed to capitalize on a first-and-goal from the 5.
It was that type of day for the Dolphins offense which once again struggled without the benefit of much of a running game.
For the first time in several weeks, the defense gave up a lot of yards, although the Dolphins did come up with four sacks and forced two turnovers in the fourth quarter.
Neither offenses did much of anything in the early going until Griese hooked up with tight end Randy McMichael for a 46-yard pass that set up Williams' 3-yard touchdown run.
Indy answered with three second-quarter field goals by Mike Vanderjagt, including a 25-yarder on the last play of the first half.
The Colts increased the lead to 16-7 on the first drive of the second half when missed tackles on a screen pass to Dominic Rhodes turned a short gain on third-and-16 into a 27-yard gain.
The drive ended with Edgerrin James scoring on a 1-yard run.
After an exchange of punts, the Colts marched 91 yards to make it 23-14, the scoring play coming on Manning's 3-yard touchdown pass to Troy Walters on third-and-goal.
It looked bleak at that point, but the Buckley interception gave the Dolphins a great opportunity to steal the game.
But they couldn't get it done, and as a result fell to 1-3 at home. They haven't started 1-3 at home since the 1968 season.
It doesn't get any easier for the Dolphins next Sunday as they travel to Nashville to take on the Tennessee Titans.