Calvert-Lewin powered home a header from Ademola Lookman’s pinpoint cross on 87 minutes to break the deadlock against an obdurate Palace side.
Fellow substitute Cenk Tosun struck just a minute later to wrap up the points at Goodison Park, lashing past Eagles’ keeper Wayne Hennessey after latching onto Michael Keane’s through ball.
In their past three top-flight matches, Everton have scored seven goals and conceded just one, with Silva’s side producing a series of enterprising attacking displays.
Against Palace, the Blues fired in 20 shots, won 10 corners and had 60 percent of the possession.
Calvert-Lewin is convinced the manager’s forward-thinking philosophy will see the Blues continue to fashion opportunities and score goals.
“We're playing extremely attacking football and I think, as a striker, you're getting chances now,” he said. “I've come off the bench against Palace and, in a short period of time, I've got my chance and taken it.
"As a striker, you want chances and you want to be allowed to get yourself in those positions.
“With the kind of football we're playing now and the quality we've got up at the top of the pitch, we're creating those opportunities and I'm happy to be there to hit the back of the net.
“The manager told me to play my natural game. The game was opening up and it’s my job to stretch it, get forward and be in the box ready to put it in when the ball comes in – and thankfully Ademola’s put a good cross in.
“I got my one chance and put it away. That’s what I want to do and that’s what I’m here to do – I’m a striker and I want to score goals.”
Calvert-Lewin says he is determined to seize every opportunity he gets to impress, as he strives to fight his way into the boss’s starting XI.
"All I can do coming off the bench is affect the game and score the goals so hopefully that puts a question mark in the manager's mind,” he said.
"I'll be doing the same as I have been in training this coming week to try to get myself in the team for the next weekend.
“We’ve got loads of quality and everyone’s fighting for their place.”
Calvert-Lewin underlined the importance of the Evertonians’ vocal backing at Goodison on Sunday, as a rocking Goodison Park crowd roared the Blues on towards victory.
“It's always a massive help when they get behind you and you can see how powerful it can be,” he said.
"You get the goal right at the end and you can feel it erupt. It's the best feeling in the world scoring a goal when the fans go off like that.
"At home, we want to make it a fortress, and I think now that we're playing more attacking football it excites the fans a lot more and you can feel that in the stadium.”