Following a late red flag, Burton won a three-lap dash to the finish line for his fourth career win in 251 starts.
Marlin, who received hate mail and death threats from people who blamed him for the crash that killed Dale Earnhardt at last year's Daytona 500, appeared to have his third victory in "The Great American Race" in hand.
With six laps to go, Marlin had spun out Jeff Gordon as a pack of cars crashed behind them, then beat Burton back to the yellow flag by less than half a car-length.
NASCAR stopped the bizarre, crash-marred race to give the remaining leaders a chance to race for the win. With the cars halted on the backstretch, Marlin got out of his car to check for damage on the right front fender.
He started to pull the bent sheet metal away from the tire, but an official warned him to get back in his Dodge. That little attempt to fix the damage was enough for NASCAR to penalize him, sending his car back to the rear of the lead pack after the cars restarted.
"I tried to get it pulled off, but NASCAR didn't like it, and they sent me to the rear," Marlin said.
Burton called the last three laps "nerve-racking."
"I didn't even look at the flag," he said. "I wasn't going to stop. When the other guys backed off, I backed off."
Following the restart, all the contenders behind Burton began to race two-by-two and even three-wide, letting the leader pull away. He crossed the finish line about three car-lengths ahead of Elliott Sadler's Ford.
Former Daytona winner Geoff Bodine, making a comeback at 52, was a surprising third, followed by Kurt Busch, 2000 race winner Michael Waltrip, Mark Martin and rookie Ryan Newman.
"A lot of what happens here is atmosphere and luck. We had some luck today," Burton said.
The 44th Daytona 500 began with some unknowns, with NASCAR giving both Ford and Dodge a quarter-inch reduction of their rear spoilers on Friday with little practice time to see how they would work in the draft.
Chevrolet and Pontiac were considered the big favorites, but the race turned into a 200-lap brawl, with lots of side-by-side action and two big crashes, one of them involving 18 cars.
Gordon, the defending Winston Cup champion who has won the Daytona 500 twice, helped ignite the big one when Kevin Harvick, last year's top rookie, tried to block him on lap 149 as the two battled for second place.
Gordon tagged Harvick's rear bumper and sent him spinning up the banking into the wall. Harvick's car then slid back down the track right in front of a pack of cars racing at close to 190 mph.
Kenny Wallace's car erupted in flames in the middle of the melee, but nobody was injured in the first big test of a NASCAR safety initiative that was accelerated after Earnhardt's death in a last-lap crash here last February.
Several drivers blamed the new aerodynamic rules for the crashinand banging in Sunday's race, saying they were forced to block continuously or lose positions in bunches.
"There's no give, just take, take, take," said Todd Bodine, who was caught up in the 18-car crash. "When you have something like that all day, something like this is bound to happen."
Seventeen cars were still left on the lead lap after that crash and the hard racing continued.
It appeared Gordon had everybody right where he wanted them when, with Marlin pushing his Chevy from behind, he passed Busch for the lead on lap 177. Marlin followed into second.
It stayed that way until after another flag for a crash by Robby Gordon on lap 191. On the restart on lap 195, with cars crashing well behind them on the main straightaway, Marlin tried to pass Jeff Gordon on the low side.
Gordon slid over to block and the two came together, with Gordon sliding sideways and skidding into the infield grass, ending his shot at another Daytona win. He continued but wound up ninth.
"I probably should have given it up once he got beside me," Gordon said. "That was my own fault. ... He had a run on me and I blocked him and got myself turned.
"It was a wild and crazy race. I went from the back to the front and the front to the back," Gordon said.
Burton, who led only the last four laps, averaged 142.971 mph to give Dodge its first Daytona 500 victory since 1974. Although NASCAR's new aerodynamic rules were intended to put a premium on passing, there were 20 lead changes among 12 drivers and plenty of excitement for the 190,000 spectators at Daytona International Speedway and the big national television audience.
Two of the top contenders were eliminated from contention early, with the engine in Tony Stewart's Pontiac blowing on the third lap, and two flat tires and an accident relegating Dale Earnhardt Jr. to 29th.
Two of the most watched drivers in the race also had their problems. Shawna Robinson, the second woman ever to race here and the first since 1980, finished 24th in only her second Winston Cup start, and 60-year-old Dave Marcis ended his long career with a 42nd-place finish in his record 33rd Daytona 500 start.
"At one point, we ran out of fuel. That didn't help us any," said Robinson. "It was kind of survival. I think my head is still spinning a little.
"We accomplished something, but I want to be competitive," she said.
Marcis, the oldest driver ever in this race, went out with an overheated engine.
"We didn't want it to end like this," he said.
By Mike Harris
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