1120 GMT May 25, 2019
The Englishman headed into the final day knowing a top-12 finish at Royale Jakarta Golf Club would see him overtake American Brooks Koepka, BBC wrote.
But he posted a three-over-par 75, including a triple bogey, to miss out on a tie for 12th by one shot.
Thailand's Poom Saksansin finished on 20 under par to win by three strokes.
Saksansin won from compatriot Jazz Janewattananond, with Sweden's Henrik Stenson another three shots back on 13 under.
Rose became world number one for the first time in September, becoming the fourth Englishman to do so after Sir Nick Faldo, Lee Westwood and Luke Donald.
The Olympic champion and 2013 US Open winner lost top spot to American Dustin Johnson later that month and has since tussled with US Open and PGA Championship holder Koepka to be ranked as the world's best.
After two rounds of 68 before a 71 on Saturday, Rose was tied for fourth at nine under par heading into Sunday's play and looked well placed to regain top spot.
However, the 38-year-old carded two bogeys and a double bogey in his opening five holes, before briefly pulling himself back into contention with birdies either side of the turn.
Rose's round unraveled once more at the par-five 12th, carding a triple-bogey eight and following that up with another dropped shot at 13.
He clawed three strokes back in the final five holes, closing out with successive birdies, but that was only enough to secure a tie for 17th place at six under par.