England drew first blood with just two minutes on the clock through Farrell, who slotted a penalty between the posts to claim his first points in an England U20 shirt. But Scotland hit back almost immediately through a penalty of their own, scored by No. 10 Duncan Weir.
England soon replied themselves, Farrell again scoring three points to make the score 6-3 with seven minutes on the clock.
Yarde then secured England's first try of the game, and his second of the tournament, minutes later, intercepting a loose Scottish pass in the English half before showing great pace to run the length of the pitch and touch down, with Farrell converting.
Scotland reduced the deficit through a long-range drop goal before Wade touched down a delicate grubber kick from Farrell after London Wasps centre Elliot Daly opted for a quick line-out, and Farrell converted to make the score 20-6 at the break.
Scotland opened the try scoring in the second half when scrum half Sean Kennedy rounded off a tidy team move to cross the whitewash between the posts, with Weir converting.
Things could have got worse for England but for a try saving tackle from replacement No. 10 George Ford, who was able to tackle his opposite number into touch when Scotland had men over.
Ford was then instrumental in England's third try of the game, setting up No. 12 Ryan Mills to score near the posts with a nice inside pass, but Ford's resulting conversion attempt hit the post. Scotland hit straight back, scoring a try of their own two minutes later through wing Kerr Gossman.
With seven points in it at 25-18, Ford missed a kickable penalty before Wade grabbed his second try, showing a great burst of pace to touch down out wide to give England breathing space at 32-18.
As Scotland pressed forward, replacement No. 8 Alex Gray picked up a pass in the middle of the park and surged forwards before picking out Wade who went over to complete his hat-trick.
Ford's successful conversion out wide bought the game to a close and England now turn their thoughts to South Africa in their final Pool C game