In front of healthy crowd of almost 5,000, Scotland took an early three-point lead through the boot of Tommy Allan, who plays his rugby in South Africa with Western Province.
Great interplay from the backs on a boggy pitch freed up space for Worcester wing Howard with 20 played, but he became outnumbered and Scotland cleared their lines.
England began to apply pressure and with Scotland down to 14 men the dominance finally told. England's pack pushed the Scottish forwards back once too often and the referee awarded a deserved penalty try, Slade added the extras.
The visitors came straight back though, and a long range penalty from Allan made it 7-6 with 34 on the clock and that's how it stayed until the break.
After a fractious start to the second period, England eventually got points on the board with 60 played, Slade again scoring a penalty. Prop Kyle Sinckler did his best to add to the scoreboard, but he couldn't quite latch onto his own chip and chase.
Slade saw two penalties miss and the impressive Anthony Watson was forced off after taking a knock as the second half continued, and it took until the 74th minute for England to put some clear daylight between themselves and the visitors.
Cowan-Dickie showed brute strength to force his way over the line, his third try in England Under 20 colours, and the nine-point gap at 15-6 remained until the final whistle.
Captain Jack Clifford was quick to stress that a win's a win, particularly in difficult circumstances: "We didn't play as well as we can and that's a credit to Scotland," he said. "The pitch began to cut up and it wasn't easy to play the quick rugby we know that we can. But we're happy with the win and it gives us something to build on."
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England Under 20 starting XV to play Scotland
15 Anthony Watson (London Irish)
14 Jack Arnott (Exeter Chiefs)
13 Harry Sloan (Harlequins)
12 Sam Hill (Exeter Chiefs)
11 Ben Howard (Worcester Warriors)
10 Henry Slade (Exeter Chiefs)
9 Alex Day (Northampton Saints)
1 Luke Cowan-Dickie (Exeter Chiefs)
2 Max Crumpton (Saracens)
3 Kyle Sinckler (Harlequins)
4 Elliott Stooke (Gloucester Rugby)
5 Dom Barrow (Leeds Carnegie)
6 Ross Moriarty (Gloucester Rugby)
7 Joel Conlon (Exeter Chiefs)
8 Jack Clifford (c) (Harlequins)
16 Danny Herriott (Northampton Saints) on for Luke Cowan-Dickie 76 mins
17 Danny Hobbs-Awoyemi (Northampton Saints) on for Max Crumpton 57 mins
18 Scott Wilson (Newcastle Falcons) on for Kyle Sinckler 62 mins
19 Tom Jubb (Saracens) on for Elliott Stooke 75 mins
20 Gus Jones (London Wasps) on for Joel Conlon 75 mins
21 Nathan Fowles (Sale Sharks) on for Alex Day 53 mins
22 Will Hooley (Northampton Saints) on for Anthony Watson 69 mins
23 Mark Jennings (Sale Sharks) on for Ben Howard 53 mins