Carlo Ancelotti's side finished with seven points from three matches, two clear of Saudi Arabia's Al-Hilal, who defeated Pachuca 2-0 in the day's other group fixture. Salzburg, with four points, and bottom-placed Pachuca, who failed to register a point, were eliminated.
Madrid will now face Juventus, runners-up from Group G, on Tuesday at the Hard Rock Stadium in Miami. Al-Hilal are set to meet Manchester City in Orlando on Monday.
Played in steady rain at Lincoln Financial Field in Philadelphia, Madrid dominated possession and tempo against a Salzburg side that struggled to create meaningful chances. Despite the weather, it was Vinicius who brought the game to life.
The Brazilian forward was denied early on by Salzburg's 18-year-old goalkeeper Christian Zawieschitzky, who produced a sharp point-blank save. Vinicius continued to threaten, and Gonzalo Garcia also went close from a low cross by the winger midway through the first half.
The breakthrough arrived in the 40th minute. Jude Bellingham's incisive pass split Salzburg's defense, and Vinicius did the rest - gliding past two defenders before rifling in a low shot from the edge of the area.
Vinicius was involved again in first-half stoppage time, collecting a loose ball inside the box and delivering a clever backheel assist for Federico Valverde, who made it 2-0 from close range.
Madrid remained in control after the break but were wasteful in front of goal. The third came late, with Garcia capping off a counter-attack by lofting a calm finish over the onrushing keeper in the 84th minute.
Speaking post-match, Vinicius said: "I'm happy with the goal and the assist, but now comes the most important part - the knockouts. We're feeling good and ready."
Madrid are also expected to be bolstered by the return of Kylian Mbappe for the knockout stages. The French forward, who missed the group phase due to illness, resumed full training on Wednesday. Head coach Xabi Alonso confirmed the decision to rest him against Salzburg was precautionary, with a view to full fitness for the next round.
With Vinicius in top form and Mbappe nearing a return, Real Madrid appear well-positioned for a deep run in the tournament.
Real Madrid have secured the signature of 17-year-old Argentine sensation Franco Mastantuono from River Plate, outmaneuvering fierce competition from Barcelona, Manchester United, and Paris Saint-Germain.
Paris Saint-Germain sealed their passage to the quarter-finals of the Club World Cup with a comfortable 4-0 win over Inter Miami on Sunday.
Chelsea secured their place in the Club World Cup quarterfinals with a 4-1 extra-time victory over Benfica on Saturday, in a last-16 clash disrupted by severe weather and defined by late drama.
Estevao has opened up about feeling anxious ahead of his high-profile move to Chelsea from Palmeiras as the two sides prepare to meet in the Club World Cup quarterfinals on Saturday.
