Enzo Fernandez was sent off in the 93rd minute for a reckless second-yellow-card challenge on Pau Cubarsi, leaving Argentina to play the remainder of normal time and all of extra time with 10 men.
Spain made the numerical advantage count just after the restart, with Torres, a second-half substitute, powering home from close range in the 106th minute after Nico Williams headed Pedro Porro's cross into his path.
The aftermath of the final whistle turned chaotic. Nahuel Molina appeared to throw a punch at Rodri, while Leandro Paredes, who had come on as a half-time substitute, was seen kicking Eric Garcia to the ground before shoving him back by the neck when the Barcelona defender attempted to confront him.
Paredes was also involved in a separate altercation with Gavi and was eventually sent off following the full-time whistle, having escaped several other bookable offences during his cameo appearance. Elsewhere on the pitch, Spain's players had already begun their jubilant title celebrations, largely unaware of the chaos unfolding elsewhere on the field.
Speaking after the match, Torres reflected on the pressure of playing against Lionel Messi's Argentina in the final.
"When you have Messi on the other side, well, you are nervous," he said. "At the end of the day, we always depended on us. We always come up with our football, and we showed it again."
Asked about his decisive goal, Torres added: "The goal belonged to 47 million people. It wasn't just mine or the 26 players. Destiny was written, and it was meant for us to win far away from our people."
Head coach Luis de la Fuente, who at 65 became the oldest coach to lead a team to a World Cup title, kept his own reaction brief.
"We are world champions," he said.
Spain finished the tournament having conceded just a single goal, the fewest of any World Cup winner despite playing eight matches, more than any previous champion, as they added the World Cup to the European Championship they won in 2024.
The match itself had been a largely cagey affair before the late drama, with Argentina goalkeeper Emiliano Martinez repeatedly called upon to deny Spain, who dominated possession and created the majority of the clearer chances without finding a breakthrough in normal time.
Messi, playing what is widely expected to have been his final World Cup match, touched the ball only sparingly as Argentina's title defence fell just short, with the South Americans failing to register a single shot on target across the full 120 minutes.
Spain's triumph completes a remarkable period of dominance for De la Fuente's side, who follow their 2024 European Championship win with a second World Cup title, matching the achievement of the golden generation that won the tournament in South Africa 16 years earlier.