Brash, a two-time overall LGCT winner, triumphed in a seven-fence jump-off by putting down a clear round with his mare Ursula XII in a winning time of 38.65 seconds.
At the huge Campo Marte grass arena in the heart of Mexico City, Germany's Daniel Beusser and Tobago Z finished second in 40.31 seconds while Italy's Alberto Zorzi and Contanga took third place in 40.37 seconds.
"I'm ecstatic about this win," Brash told the crowd at the trophy ceremony. "Ursula, she is 17, and this win means a lot to us all.
"The crowd are incredible here, they really get behind us all and they've really made it a special venue for us."
Starting fourth in the eight-rider jump-off, the Scot shaved more than a second off the leading time set by Germany's Beusser, as he produced a fast-paced yet smooth ride in front of a boisterous crowd of 20,000 in temperatures of 28 degrees Celsius (82 Fahrenheit).
The next rider, Jerome Guery of Belgium, went for broke as he put down the fastest start time, only for his horse to refuse to jump the fourth fence.
The sixth rider, Eric Lamaze of Canada, would have won as he produced the fastest round in 37.52 seconds, but took too much risk on the final jump, which led to an error.
"This ring is fantastic for her, I can use her strength, which is her stride," said Brash, the Olympic team champion at the London Olympics who now leads the overall LGCT standings with 40 points.
"It was still a very competitive jump-off but we've done our best and I thought she jumped her best in the jump-off."
Brash, the overall winner in 2013 and 2014, is trying to become the first three-time champion in GCT history.
Australia's Edwina Tops-Alexander, the only other rider to have won the overall title twice, didn't qualify for the jump-off after her horse made two errors on the final triple combination in the first round.
Global Champions League
Earlier on Saturday, the newly formed Miami Celtics took their first win in the Global Champions League team competition, just ahead of Paris Panthers in second place and Valkenswaard United in third.
Although the Paris Panthers had been in pole position after the first round on Friday, they were unable to fend off the Miami Celtics thanks to a double clear by Irish riders Denis Lynch and Michael Duffy in Saturday's second round.
"I'm lost for words -- to come to a beautiful place like Mexico with a new team was unbelievable," said Duffy, the Under-25 rider on the Celtics team. "We delivered the goods today, and the plan is to stay at the top."
Mexico City hosted the first of the 16 legs in the 2018 series as the Global Champions Tour and League builds towards the final in Doha and the new GC Prague Play Offs in December.
The high altitude of Mexico City proved too much for the reigning champions, the newly renamed Montreal Diamonds, who finished in eighth place.
"It's a very nice course but we didn't jump our best today," Montreal Diamonds rider Lamaze said after he produced eight penalties in the first round with Chacco Kid.
"It's our first outdoor show and our horses were a bit impressed, but that's the game. There were faults everywhere so compliments to the course builder."
The 19 GCL teams are all vying to reach the inaugural GC Play Offs in Prague just before Christmas, which will see the winning team claim $3 million.
Prague will also host to the first Longines Global Champions Super Grand Prix, in which the winners of each LGCT event throughout the year will compete against each other.
But first, the Tour will head to Miami Beach between April 5 and 7 before traveling to Asia for the Shanghai leg on April 20-22.