The Australian was almost the last man standing after Chinese skater Li Jiajun triggered a mass tumble on the last turn.
Among the fallen was American medal hope Apolo Anton Ohno, who clambered to his feet to take silver.
The bronze medal went to Mathieu Turcotte of Canada, while Li was disqualified.
smiles on you some days and this is my day"
Bradbury, a 28-year-old from Brisbane, was thanking his lucky stars as he coasted over the finish line from last place after taking advantage of the last lap pile-up.
"It's good, but it doesn't feel right you know," he said with great honesty after the race.
"I wasn't as strong as the other guys out there, but I am going to take it.
"I came to these Games hoping to make up for opportunities where I didn't skate my best. I consider myself the luckiest man.
"God smiles on you some days and this is my day."
The Australian looked as though he would have no chance of a medal as the other four skaters in the final battled for the places.
But all four came tumbling down when Ohno appeared to get barged by China's Li Jiajun going into the final bend.
Bradbury was left to cross the line as the winner in one minute 29.109 seconds.
Ohno finished in 1:30.160 while Turcotte clocked in third in a time of 1:30.563.
Bradbury had enjoyed similar good fortune in his semi-final when he had been trailing before coming through on the fly because the referee ruled he had been impeded.
Although this was his third Olympics, he had never made it through to the quarter-finals of the 1,000m before.
But he did win a short track relay bronze for Australia at Lillehammer in 1994.