Fabian Ruiz gave Spain a deserved lead with a tight finish from inside the box in the 30th minute, only for Belgium to equalise before half-time through a brilliant header from Charles De Ketelaere. The Red Devils, already missing suspended captain Youri Tielemans after he was injured in the warm-up, then lost goalkeeper Thibaut Courtois to injury in the second half.
The game looked destined for extra time until Merino, introduced from the bench in the 86th minute, struck again just two minutes later. Substitute goalkeeper Senne Lammens failed to hold on to a speculative effort, and Merino pounced on the rebound to send Spain through 2-1 and set up a semi-final meeting with France in Dallas on Tuesday.
Speaking to La1 immediately after the final whistle, an emotional de la Fuente praised his squad's resolve.
"This is the character of the team in any circumstance and situation," he said. "I reiterate my pride in leading this team, which wants to grow and improve. We did more than enough to win more comfortably. You have to realise how difficult it is to win; you have to give that its due value."
Asked about matchwinner Merino, the coach was effusive: "What he does is incredible, he has many qualities, he's world class, he could play for any team and we're lucky to have him. We know that whenever we need him, he's there."
On France, he added: "It's fair to think we're going to work to overcome them. We're the only side to have beaten them in two consecutive matches. A truly great national team is going to face another great national team."
In his press conference, de la Fuente opened with a message unrelated to the football.
"We want to pass on our condolences and share the pain of the victims of the fire in Almeria," he said. "And during the match, the mother of our photographer, Angel Martinez, passed away."
Asked whether the semi-final amounted to an early final against France, he said: "We're two of the national teams that everyone thought could get here. We had high expectations, but we're aware that we're the only team that has been able to beat France in two semi-finals. The match will demand we're at our very best."
Reflecting on a 13-match unbeaten run across recent Euros and World Cups, he added: "With gratitude to all the players I've had, to my staff, to those who work with me. And you work better happy than angry. I'm a lucky man. I couldn't have got here on my own."
In the mixed zone, Nico Williams reflected on a personally difficult year.
"I feel liberated," he said. "The year has been miserable. But life knocks you down and you have to get back up, to help the team."
Asked who had helped him through it, an emotional Williams said: "The group, they've supported me from the first moment. My family is there with unconditional love, my brother and my girlfriend. It's a source of pride and I don't want to say any more or I'll get emotional."
Lamine Yamal, meanwhile, was satisfied with the level of Spain's performance.
"We were superior," he said. "The goal was a strange feeling because just when we were at our best, they scored, but no team has gone toe-to-toe with us." On the France test to come, he was defiant: "If anyone has to be afraid, it's them. We're two great teams, for me the two best, but we have no fear at all."
Spain's win means Belgium's so-called "Golden Generation" bow out of the tournament, while France, who beat Morocco 2-0 on Thursday to become the first side to book their semi-final spot, remain unbeaten through five matches so far in the United States.