The United States played with 10 men after a disputed red card but but kept control of the match on Thursday.
Commentators hailed the result as a historic breakthrough and a performance that reinforced belief within Mauricio Pochettino's squad that it could compete for the title.
Coverage showed strong enthusiasm. Analysts highlighted what they described as the historic weight of the night.
The victory marked the United States' first knockout‑stage win since the 2002 World Cup, and its first win against a European team in five years. It also marked the first World Cup in which the United States has earned three wins.
The Wall Street Journal linked the triumph in Santa Clara to the country's 250th anniversary.
The newspaper wrote that, after once failing to qualify for the World Cup for four decades, the United States is shedding the limitations of the past and using the tournament to redefine its place in global soccer.
'Temptation to look ahead'
The WSJ noted that Belgium awaits in the round of 16, with possible meetings against Spain and France later in the tournament, concluding that "the temptation to look ahead has rarely been stronger."
The Athletic echoed Pochettino's call to "reach for the moon."
The outlet described a squad driven by belief and ambition, arguing that history no longer limits the team and that unprecedented achievements are no longer beyond its reach.
Analysts also praised the team's style of play and preparation.
The Athletic said the United States dominated a World Cup knockout match for the first time.
Fox Sports wrote that Bosnia and Herzegovina had no answer to the hosts' pace, with the Americans enjoying 63-percent possession.
Yahoo Sports called the United States the best counter-pressing team in the tournament.
Bleacher Report highlighted the team's composure after leading scorer Folarin Balogun was sent off following a disputed red card.
Balogun had given the United States a 1-0 lead just before halftime with his third goal of the tournament.
Folarin Balogun. Photo: EPA/BENJAMIN FANJOY
Brazilian referee Raphael Claus. Photo: EPA/BENJAMIN FANJOY
Yahoo Sports noted that Balogun celebrated his goal with a gesture used by basketball star LeBron James.
James later praised the striker and encouraged the team in a post on X.
Some political commentators noted that Balogun, who was born in New York and raised in London by Nigerian parents, would not have been eligible to represent the United States if President Donald Trump's proposal to end automatic birthright citizenship had been in effect.
Balogun scored two days after the US Supreme Court struck down Trump's executive order seeking to restrict birthright citizenship, known by the Latin term jus soli.
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Source: IAR, PAP