Culpepper had another uneven outing, but he did score the Dolphins' only touchdown of the game when he scrambled in from 5 yards out in the third quarter to give Miami a 10-7 lead.
The Titans tied the score at 10-10 later in the quarter when they took advantage of a Welker fumble on a punt return and got a 22-yard field goal from Rob Bironas.
Tennessee appeared to take the lead in the fourth quarter when Pacman Jones returned a punt for a touchdown, but the play was called back because of a penalty.
The Daniels interception was one of three takeaways on defense, and that turned out to be the difference in the game.
As big as the Daniels play was, an even bigger might have been Andre Goodman's fumble recovery near the goal line when it looked like Tennessee was ready to take a 14-3 lead.
But Tennessee answered back with a 27-yard touchdown pass from Kerry Collins to tight end Bo Scaife.
It was Scaife who fumble near the goal line as he was running toward the end zone after catching another pass from Collins.
Will Allen came from the side to knock the ball loose from Scaife and Goodman scooped up the fumble.
Offensively, things again were a struggle and even the touchdown drive wasn't without its problems.
The Dolphins thought they had scored when Culpepper hit Chris Chambers and he backed into the end zone, but despite one official's initial indication of a touchdown, the final ruling became that Chambers was down inside the 1-yard line.
Ronnie Brown then was stuffed for no gain on first down and on second down Jason Taylor, in the game as an extra tight end, was called for a false start.
Culpepper finally scored on second-and-goal.
It was a tough way to get a touchdown, but as Sunday's game indicated nothing is coming easy for the Dolphins so far this season.