The five-year-old defied a wide draw to give trainer Saeed bin Suroor his ninth success in the feature of the world's richest raceday.
"The Dubai World Cup has been extremely kind to me and to have the pleasure of training a horse like Thunder Snow is something that's hard to describe," Bin Suroor told The National.
"I have always dreamed that he could win one World Cup, but to become the first horse to win two is something I am finding hard to believe."
Favourite Capezzano and Gronkowski made the early running ahead of Thunder Snow, but the defending champion stayed on under pressure from jockey Christophe Soumillon to overhaul Gronkowski in the dying strides and win by a nose after a photo finish.
"Last year I won by five, six or more lengths and today I had to fight hard," jockey Soumillon told the Racing Post. "The two horses in front were going a bit better than me, but I gave him a chance."
The 4/1 shot landed the $12 million prize for Godolphin owned by Dubai ruler Sheikh Mohammed.
Gronkowski, named after NFL star Rob Gronkowski who retired earlier this week, had to settle for second at odds of 28/1 despite leading for much of the mile and two furlongs, while Gunnevera (12/1) was a distant third as Capezzano slipped out of contention.
"It was very hard to get by Gronkowski," added Frenchman Soumillon.
"I was looking more like a Cheltenham jump jockey in the end instead of an American-style jockey, but you need to keep him going and do something different."
Earlier on Saturday, Cross Counter appeared for the first time since landing last November's Melbourne Cup to win the Dubai Gold Cup for English trainer Charlie Appleby.
Appleby, who also sent out runner-up Ispolini, suggested his talented four-year-old would now be aimed at the Ascot Gold Cup at the Royal meeting in June.
The trainer was relieved his Sheikh Mohammed-owned stable star has not shown any ill effects from his Melbourne Cup adventure.
"It was a tough ask to go to Australia as a three-year-old and win the Melbourne Cup - it's always in the back of your mind whether it took a bit out of him," he said.
"But this was our first opportunity to run him since then and he's answered all the questions we need to know."
Japan's cherished dream of finally winning the Prix de l'Arc de Triomphe after years of heartache moved a step closer to reality when the brilliant Almond Eye won the Dubai Turf.
The four-year-old Japanese Triple Crown winner has the French showpiece in October as her likely ultimate objective after easily fending off another Japanese contender Vivlos under French rider Christophe Lemaire.