Trained by Bob Baffert, the odds-on favourite, made a dramatic comeback in the 2,000-metre contest after breaking from the stalls at the back of the pack.
"It was like watching Seabiscuit or something. It was a Hollywood-type finish," Baffert told reporters at the 60,000-capacity Meydan racecourse.
Neolithic came third of the 14 runners in the contest, which was the world's richest horse race until being surpassed by Florida's $12-million Pegasus World Cup earlier this year.
Smith rode off the track after the win with the Saudi flag of owner Prince Khalid bin Abdullah draped around his shoulders.
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"Once we got away like that and got squeezed leaving there, I had no choice but to just sit there and let him collect himself," Smith said.
"When I called on him heading for home, he just took off. It was just incredible, just incredible."
(Reporting by Stephen Kalin, editing by Pritha Sarkar)
