Montoya, making the jump from Formula One to NASCAR's Nextel Cup series this year with the Ganassi team, chased and caught former IRL champion Dixon, who was struggling with brake problems after building a nearly full-lap lead on the 3.56-mile road circuit.
As expected, the fast Daytona Prototypes were dominating the twice-around-the-clock race, with the two Ganassi Lexus Rileys leading the way in the early going.
With Dixon fading, NASCAR champion Jimmie Johnson drove into second place in a Pontiac Riley prototype and Darren Law was third in a Porsche Riley, all within a lap of the lead car shared by Montoya, Scott Pruett and Salvador Duran.
Four-time NASCAR champion Jeff Gordon, co-driving another Pontiac Riley, was 20th.
Tony Stewart, another former NASCAR champion, has come close enough to winning this race twice that he knows just how disappointing the grueling event can be.
"It can be brutal," Stewart said minutes before the start. "It can just eat you up. We came within 17 minutes of winning this thing a couple of years ago and it just blew up on us. There are just so many things that can go wrong in 24 hours, you just have to drive the car and put everything else out of your mind."
Stewart, co-driving a Pontiac Crawford - one of 28 Daytona Prototypes at the front of the star-studded 70-car field - with road racing stars Andy Wallace and Butch Leitzinger, was among the favorites as the grueling race got under way under a mostly sunny sky with temperatures in the low 70s.