Brazil only managed a 1-1 tie against Switzerland in the country's first game of the 2018 tournament.
Neymar dropped to his knees after the final whistle, sobbing in his hands as his teammates surrounded him and then lifted him off the ground.
"The great merit of this team was not giving up at any time", Silva said.
Barcelona playmaker Coutinho gave Tite's in-form side a first-half lead in spectacular fashion in its Group E opener against Switzerland but the European side was able to baton down the hatches and escape with a draw after Steven Zuber's 50th-minute equaliser.
"This World Cup isn't being (easy) for anyone", Gabriel Jesus said.
The competition's most decorated nation were in danger of failing to win either of their first two games in Russian Federation before Coutinho prodded in a stoppage-time opener and Neymar added a second in a 2-0 success. If Nigeria wins, it will advance to the round of 16.
This was just his fourth appearance since breaking a bone in his foot against Marseille in February and only the second time he has completed the full 90 minutes.
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"We had a plan, strategy, idea to control the opponent with and without ball", Costa Rica coach Oscar Ramirez said.
Beside Uruguay, no other South American team had won a match until Brazil did so on Friday.
Kolarov, whose stunning free-kick saw off Costa Rica, stressed Serbia will maintain its intensity when the Balkan nation faces Switzerland in Kaliningrad on Friday. The wonderful video is going viral on the internet for all the right reasons.
The African side will secure a spot in the knockout stage if they beat Argentina on Tuesday in Group D's final round of fixtures.
Neymar, receiving from Philippe, nearly scored before he took out Keylor Navas amid scramble.
The much-anticipated match between Brazil and Costa Rica ended with victory for Brazil at 2-0.
Although left back Marcelo had an average game in defense, his constant runs down the flanks ultimately helped when his risky cross led to the opening goal.
"I returned the ball because it was not this ball that was going to win us the game".