Casemiro, 30, was at his best in Selecao's 1-0 victory on Monday, 28 November.
Tite's men were creeping towards dropping points for the first time in this year's campaign in Qatar.
However, the Manchester United midfielder was the difference maker after he lashed home a phenomenal 83rd-minute strike.
His goal sent Selecao into the last 16 of the FIFA World Cup.
It was an incredible effort from the former Real Madrid man, who has been a standout performer for Brazil so far in Qatar.
He made five passes into the final third against Switzerland, along with four interceptions and six recoveries.
Tite's side now head to the last 16 with a game left to play against Cameroon on Friday, 2 December.
Casemiro was equally as impressive in Selecao's 2-0 victory over Serbia in their opener.
Neymar, who sat out the win over the Swiss due to a foot injury, has lavished praise on the Manchester United midfielder.
The Paris Saint-Germain attacker said:
"Casemiro has been the best midfielder in the world for a long time."
Casemiro left Madrid after seven years at the Santiago Bernabeu, where he became a Los Blancos legend.
He made 336 appearances, scoring 31 goals, providing 29 assists, and winning the Champions League five times as well as the La Liga title on three occasions.
The Brazilian midfielder joined United for €70.65 million and has made 18 appearances for United, scoring one goal and providing an assist.
Many had debated the price the Red Devils paid to lure him to Old Trafford.
However, with each passing game for club and country, Casemiro gives credence to Neymar's assessment that he is the top midfielder in world football.
Brazil manager Tite wants players to stop fouling Neymar at the FIFA World Cup
Neymar picked up an unfortunate foot injury in Selecao's FIFA World Cup opening 2-0 win over Serbia.
The PSG forward was fouled nine times before being withdrawn in the second half, and he will no longer play any part in Selecao's group-stage action.
His manager Tite has called on players to stop targeting the former Barcelona man.
Neymar was in red-hot form heading into the FIFA World Cup, scoring 15 goals and contributing 12 assists.
Fans are disappointed not to witness the Brazilian attacker at his best for the time being.
So too is the Brazil manager as he said regarding Neymar being targeted (via the Guardian):
“If you want to celebrate the football you have to pay attention to the fouls. They target specific players and this is the effect. It has to be stopped.”