Australia took an early lead in the corner through wing Andrew Kellaway, which was brilliantly converted by Jake McIntyre with England wing Nathan Earle bearing down.
But England hit back with a quick double from scrum half Taylor. First he sniped between two from close range before No. 8 James Chisholm found him on the inside to dive over.
Australia made it 17-10 after 30 minutes with a McIntyre penalty before a brilliant piece of skill from Nick Tompkins found Saracens teammate Earle, who powered his way over the line to give England a 24-10 advantage.
Australia hit back through Kellaway, who grabbed his second try before the break, but England started the second 40 with a bang as Jones dived over for the seventh try of his England U20 career.
Again Australia came back fighting though, and scored through McIntyre to make it a seven-point game at 31-24.
However, Earle killed off the contest when he crossed for his second try - and fifth of the competition - in the corner following some more neat work from Tompkins.
Thanks for all the messages. A tough game but a great result! All credit to the boys one hell of a shift !- Billy Burns (@BillyBurns10) June 6, 2014
Captain Maro Itoje said: "Australia are a top side and coming into the game we had nothing but the utmost respect for them - they threw a lot at us but I thought we coped well.
"We really pulled together and showed a lot of heart and passion to get that result. I'm really happy with how the team performed, but again we feel that there's still more to give.
"It was great to have the support of the seniors at the game. That meant a massive amount to the boys and we're looking forward to watching their game tomorrow and then taking on Argentina on Tuesday."
Thank you all for the support was a tough game but boys all dug in great result ?- Ross Moriarty (@RossMoriarty6) June 6, 2014
Forwards Coach Ian Peel added: "It was a really good test for us - both mentally and physically. The lads know they've been in a tough game; the forwards put in some excellent scrum work and our line out functioned well. We pressured them, stole some good ball and ultimately set up a strong platform.
"The breakdown was a big target area for us and I thought we came out on top, which is ultimately why we won the game. The matches come thick and fast, we've got a few bumps and bruises so we'll recover well and get ready to go for Tuesday against Argentina."
Points: Taylor 2T, Earle 2T, Jones 1T; Burns 1P, 5C
England U20 starting XV against Australia
15 Howard Packman (Northampton Saints)
14 Henry Purdy (Leicester Rugby)
13 Nick Tompkins (Saracens)
12 Harry Sloan (Harlequins)
11 Nathan Earle (Saracens)
10 Billy Burns (Gloucester Rugby)
9 Henry Taylor (Loughborough University)
1 Danny Hobbs-Awoyemi (Northampton Saints)
2 Tom Woolstencroft (Bath Rugby)
3 Paul Hill (Leeds Carnegie)
4 Maro Itoje (Saracens, captain)
5 Charlie Ewels (Bath Rugby)
6 Ross Moriarty (Gloucester Rugby)
7 Gus Jones (London Wasps)
8 Joel Conlon (Exeter Chiefs)
16 Jack Walker (Leeds Carnegie) on for Tom Woolstencroft 68 mins
17 Alex Lundberg (London Wasps) on for Danny Hobbs-Awoyemi 68 mins
18 Harry Rudkin (Leicester Tigers) on for Paul Hill 73 mins
19 Hayden Thompson-Stringer (Saracens) on for Gus Jones 71 mins
20 James Chisholm (Harlequins) on for Joel Conlon 9 mins
21 Callum Braley (Bristol Rugby) on for Henry Taylor 57 mins
22 Sam Olver (Northampton Saints) on for Billy Burns 65 mins
23 Aaron Morris (Bedford Blues) on for Howard Packman 40 mins