Fleetwood came home in 30 for a second consecutive round of 65 on Saturday to sit at 13 under but Rose matched him to be two shots better off and one ahead of Dylan Frittelli and Jon Rahm.
The former US Open champion leads the DP World Tour Championship by a single shot ahead of today's fascinating final round.
Rose needed to finish at least solo fourth, but the birdie only gave him a tied fourth place at 17-under par.
The season finale at Jumeirah Golf Estates was won by Spain's Jon Rahm, after he followed his impressive round of 65 on day three with a 67 on Sunday to become the only multiple victor of a Rolex Series tournament this season.
Running on fumes as he plays his eighth event in nine weeks, Lowry had to rely on his magical short game to save pars early on the back nine before three birdies in his last four holes allowed him to sign for a 70 he felt was "one of the best two-unders I've ever shot".
Rose, victor of the European Tour's Order of Merit in 2007, could still claim the Race to Dubai title with a solo second finish so long as Fleetwood doesn't win the DP title on Sunday.
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Englishman Fleetwood, who went into the season-defining event at Dubai's Jumeirah Golf Estates course leading the race to find Europe's leading golfer of the year, shot eight birdies in his second round after his disappointing opening 73. "When I looked at yesterday's round, there were 10 opportunities I felt I didn't take, one way or another, so today was a bit sharper".
"When I step on the first tee tomorrow that's irrelevant".
"This is going to be a day just to go for it really and play well". "It's about playing good golf tomorrow. It's very special", said Fleetwood. This is a different pressure to Wentworth a year ago (the BMW PGA Championship) when I didn't want to play because I was scared I would not get it off the first tee. There were still a couple moments out there when I didn't hit great putts, but that one at the last is a big confidence builder.
"Tommy's last two rounds have been incredible and he is right there should I make any kind of mistake".
Fitzpatrick could only manage a level-par 72 to fall five shots off the pace.