The 29-year-old settled a cagey affair with a powerful half-volley from outside the penalty area in the second minute of added time, capping what Marsch described as a richly deserved reward for a player who has endured profound personal tragedy.
"I couldn't think of a more deserving human being in a group of incredible human beings," Marsch told reporters after the win in Los Angeles.
"Maybe Steph is the most deserving to have a moment like that. So I'm really happy for him, and I think from somewhere his parents are looking down, and they saw that."
Eustaquio lost both of his parents in little more than a year, his mother in April 2023 and his father in May 2024.
Marsch said Eustaquio embodied the leadership and composure his side had worked to develop.
"Steph is one of the people in the team that I think is the most reliable and understands what we're trying to achieve as a group," he said. "We talk a lot about having calmness... It was good to see him in that moment just thinking about how to strike the ball in a way to give it the best chance to go in."
Marsch said the nature of the victory would leave a lasting impact back home.
"The timing of the goal means that the win is incredibly dramatic. I think the effect that it will have in Canada and the inspiring of people will be immense," he said.
The American acknowledged his side had been disappointed to leave Canada after the group stage but said the move to Los Angeles had not proved disruptive because his team were accustomed to playing south of the border.
"We're used to playing in the States. We actually play more games in the States than we do in Canada," he said.
Canada will face either Morocco or the Netherlands in Houston on July 4th, with Marsch relishing the opportunity to test his side against one of the big guns.
"I feel like it's a free hit, and we're going to go after it and do everything we can to see if we can find a way to get a win," he said, describing Morocco as "a modern giant" and the Dutch as "a traditional giant".
Check out the match report from Canada's win with Flashscore.