Brazil's win set up a last-16 meeting with Mexico in Samara on Monday, while it is Switzerland, not Serbia, who will take on Sweden in St Petersburg the following day after drawing 2-2 with Costa Rica.
Tite's side left it late to get past Costa Rica on Friday, but they only had to wait 36 minutes for the opener in Moscow, Paulinho stabbing over Vladimir Stojkovic off a magnificent pass from Philippe Coutinho.
It was Paulinho's eighth goal since Tite took the helm in 2016 and brought his former Corinthians star back into the set-up, with only Neymar and Gabriel Jesus (10) scoring more for Brazil in the same timeframe.
The Barcelona midfielder was replaced by the more defensive Fernandinho in the 66th minute as Serbia went on the attack in a bid to save their World Cup campaign.
But Silva, the former captain who was shunned following Brazil's failure to lift the World Cup on home soil four years ago, wrapped up the win and kept hopes of an unprecedented sixth title alive.
The Selecao started positively, but had to replace Marcelo with Filipe Luis, who only returned from a broken leg last month, in the 10th minute, the Real Madrid left-back grimacing as he hobbled down the tunnel with what was later confirmed to be a back spasm.
Jesus proved lively with runs in behind the Serbia defence and his endeavour created a chance for Neymar, whose cross-goal strike was pushed away by Stojkovic.
Manchester City striker Jesus was caught on the ankle by Sergej Milinkovic-Savic in the process, but it did not appear to hinder him when he cut inside of Milos Veljkovic and saw his shot blocked behind by Nikola Milenkovic.
Adem Ljajic earned a yellow card for a late challenge on Neymar, the Paris Saint-Germain star receiving more rough treatment, and Aleksandar Mitrovic missed the target with an acrobatic attempt in the 34th minute.
The breakthrough came two minutes later and it went the way of Brazil. Filip Kostic did not track the run of Paulinho, who raced between two defenders and poked Coutinho's delivery beyond the onrushing Stojkovic.
Neymar had a low drive kept out by Stojkovic at the near post after a swift break five minutes into the second period, and Serbia responded by turning up the pressure.
Antonio Rukavina, who started in place of the experienced Branislav Ivanovic, saw his shot pushed into the danger area by Alisson and the goalkeeper was relieved to see Silva stop Mitrovic nodding the loose ball home.
A speculative cross from Milinkovic-Savic had Alisson scrambling, while Mitrovic headed a cross from Rukavina straight at the feet of the keeper in the 65th minute.
Tite replaced Paulinho with Fernandinho as he sought greater stability, but it was Silva, capitalising on shoddy marking from Nemanja Matic, heading home at the near post from Neymar's left-wing corner two minutes later that truly gave him that.
The wind was taken out of Serbia's sails and Brazil confidently saw out the final stages, Stojkovic doing well to thwart Neymar in stoppage time as the Selecao avoided the humiliating group-stage exit that befell fellow heavyweights and defending champions Germany earlier in the day.