Two late goals sealed the points for Everton, but the stage was set after Pickford kept out a penalty from Luka Milivojevic midway through the second half to keep the scores level.
"He has this quality, this profile," Silva said after the game.
"He is solid in that moment and can keep calm to take the right decision. It was an important moment in the match."
The result took Everton up to eighth in the table, and Silva is hoping they can push on with some momentum now.
"Now we are in a good momentum and it is important we keep (that)," he added.
"But we know the Premier League is really hard and every game is a different challenge and you have to be ready for everything."