The Brazilian had come under pressure for failing to hit the target after making an explosive start to his Everton career following his £40million move from Watford in the summer.
The 21-year-old had only scored once since being sent off against Bournemouth in August and Silva admitted he was considering dropping the striker.
However, his brace here takes his season's tally to six, already beating last year's haul with the Hornets.
Everton were lighting quick out of the blocks and Gylfi Sigurdsson should have put them ahead in the sixth minute but he failed to connect with Seamus Coleman's cross.
Sigurdsson repeated his mistake just moments later as Brighton we given a real let off, this time he scuffed wide from Lucas Digne's pass from the left wing.
But Silva's side did finally make the breakthrough and they did it in spectacular style with a quick break from Brighton's corner.
Kurt Zouma cleared the danger and Sigurdsson picked up the loose ball and surged forward.
He played a neat past to Bernard before receiving the ball back and playing a deft pass through to Richarlison, who hammered the ball into the roof of the net.
Everton were then denied a stonewall penalty by referee David Coote, who turned away the home side's appeals when Digne was kicked by Alireza Jahanbakhsh.
Brighton pulled a goal back in the 33rd minute when Lewis Dunk headed home from Solly March's cross following a corner leaving the scored level at the break.
Everton started the second half with the same flourish they had started the first and Idrissa Gueye saw his shot from the edge of the box strike the post.
The loose ball broke for Bernard, who crossed for Theo Walcott but he missed a sitter and shinned the ball wide with the goal at his mercy.
But there was nothing wrong with Coleman's strike on 50 minutes; a real thunderbolt that went into the bottom left corner.
The right-back celebrated his first goal in 21 months by sliding on his knees in front of the Gwladys Street Stand with his hand cupped behind his ears.
Richarlison then pounced on an awful stray pass from Dunk before racing forward, rounding Matt Ryan and squeezing the ball in from a tight angle.
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