Rose needed an eagle on the 18th to overtake Fleetwood in the standings but could only make a birdie to finish tied for fourth at the DP World Tour Championship.
Fleetwood shot a modest 74 to end on 11 under but his tie for 21st was enough to seal an overall victory.
Rahm produced a fine display to win by one shot from Shane Lowry and Kiradech Aphibarnrat. Ireland's Lowry finished with a brilliant 63 that featured 10 birdies and a bogey in what was his lowest round since 2011, as he tied for second with Thailand's Aphibarnrat, who shot a 67.
Rose, who was aiming for a third successive victory after back-to-back wins in China and Turkey, had a one-shot lead overnight and led for much of the final day.
The Olympic champion found himself in trouble on the 17th but rescued a par that kept alive his chances of a second order of merit triumph.
He then gave himself a long look at an eagle on the last but couldn't hole the putt that would have given him the overall title.
Going into the tournament, Sergio Garcia was the only other player who could have taken the Race to Dubai title - he needed to win the Tour Championship with Fleetwood finishing outside the top 20 and Rose outside the top four.
He ended with a fine 65 including eight birdies that saw him finish on 17 under in a tie for fourth alongside Rose.
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