The baby girl named Rouh, meaning Soul, suffered respiratory problems and a weak immune system, a doctor at the Emirati Hospital in Rafah said
Thomas made bookend bogeys but piled up eight birdies in between in the third round on Saturday to edge ahead of Patrick Reed and Erik van Rooyen.
On a day when overnight leader Bryson DeChambeau self-destructed, Thomas carded six-under-par 65 at Club de Golf Chapultepec in Mexico City.
Two years after losing a playoff to Phil Mickelson, Thomas has a chance to avenge that near-miss and claim a 13th PGA Tour victory.
"I really want that first place. I definitely feel like I have a bit of unfinished business here," said Thomas after posting a 15-under 198 total.
Fellow American Reed (67) hit an unusually poor bunker shot to bogey the final hole and slip back into a tie for second with South African van Rooyen (67).
American DeChambeau struggled to a 71, hitting a series of poor shots down the stretch and compounding his misery by missing several short putts as he frittered away a handy lead with three late bogeys.
He fell back into a tie for fourth with Spaniard Jon Rahm (61) and Northern Irishman Rory McIlroy (68), four strokes from the lead.
Rahm's course record, which tied his career-best score, included a hole-in-one at the 158-yard 17th, where his ball disappeared on the second bounce.
Chez Reavie also had an ace, at the 167-yard third hole, though the American ended the day 13 strokes off the pace.
Thomas on Sunday will renew his rivalry with Reed, whom he beat in a three-way playoff (along with Xander Schauffele) at the Tournament of Champions in Hawaii last month.
Reed made his share of mistakes on Saturday, but displayed a magnificent short game, at least until the final hole.
"It was a little sloppy today. I still hit a lot of quality shots but hit some shots that were question marks," said the 2018 Masters champion.
"If a sloppy day around here equals six birdies, as long as I get a bit tighter I should make a lot more."
Van Rooyen, seeking a third South African victory in the event after Ernie Els in 2004 and 2010, tried to keep his thoughts simple as he pondered the final round.
"You can't overthink this kind of stuff," said the world number 52.
"I expect to go perform my task really well. There's going to be a little bit of nerves, and if I can control that and stay in my bubble, I'll be alright."
The baby girl named Rouh, meaning Soul, suffered respiratory problems and a weak immune system, a doctor at the Emirati Hospital in Rafah said
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