The Brazilian winger netted both of his new side's goals in the 2-2 draw with Wolves at Molineux, the second coming despite Phil Jagielka's earlier dismissal.
It was a performance befitting the £40 million ($51m) the Toffees reportedly paid to sign the 21-year-old from Watford, for whom Silva originally signed him 12 months ago.
The pair are now reunited at Everton and Richarlison was quick to thank his Portuguese manager for providing him with a Premier League opportunity.
"I'm very happy for the two goals. It was a very difficult match because we had to run double," the former Fluminense man told BT Sport.
"We played with one less player after the red card and it was very difficult, but one point away... it's a very important debut for me.
"I know my responsibilities and I know also the coach has given me freedom to play my football in attack, so I know what I have to do on the pitch. I'm very happy.
Silva, meanwhile, insisted the hefty fee attached to Richarlison's signing should have no bearing on the judgment of his performances.
"When a club pays money it's because it's his value in the market," he said. "Like all the other players we sign it's not because they are [worth] more or less money. We believe in all of them.
"He performed well like all of the squad. It's important for him to score in our first match, his first official match in the shirt."