At lunch on Day 2 England were 5-61, trailing Australia's first innings total by 265 runs and still 65 short of avoiding the follow on.
England resumed on 1-8 but after 70 action-packed deliveries, they were in complete disarray having lost a further four wickets for just 17 runs to be 5-23.
Harris trapped a brainless Alastair Cook lbw with the second ball of the day, and should have been on a hat-trick after Ian Bell was given a life by Shane Watson at first slip the very next ball.
Johnson then cranked up the heat on nightwatchman James Anderson, striking him twice on his bowling hand in his first over, before dismissing him with his next.
Harris' perfect line struck gold again when Kevin Pietersen prodded another sitter to slip, only this time Watson held on to make it 4-17.
The enthralling exhibition of fast bowling lasted 45 minutes, all before many SCG patrons had found their seats.
But then it was Peter Siddle's turn to take over.
Siddle (1-4 from five) had Bell caught behind for two in his second over to ensure Australia ultimately lost nothing from Watson's earlier fumble.
Rookies Ben Stokes (23 not out) and Gary Ballance (17no) are showing fight after England at one stage looked in danger of failing to reach their lowest Ashes total of 45.
For their opening spells on Saturday, Harris had 2-6 from five overs, and Johnson 1-8 to go with the wicket of Michael Carberry he claimed late on day one.
Johnson has been man of the match on three occasions this series and now has 33 wickets.
He continued his all-out assault in his second spell, nailing Ballance viciously on the helmet and delaying play by nearly 10 minutes.
England's batsmen are mentally shot, with their top five batsmen producing a top score of 7 in the worst batting collapse of many this summer.
Cook inexplicably shouldered arms to a full and straight ball from Harris, a sign of the toll this series has taken on the English skipper.
Bell, the man of the series in the UK last year when England won 3-0, was incapable of building pressure on the Australians, mustering just two runs from 32 balls.
England batted for 23.5 overs and 115 minutes in their Sydney first innings before anyone made double figures, and at that point they were five wickets down.
A rare moment of good fortune came when England were 5-35, and the umpires decided a Stokes nick off Siddle had narrowly bounced before entering the gloves of Brad Haddin.
The wicketkeeper immediately made the umpires aware that he wasn't sure, and after one inconclusive look at a replay, the appeal was dismissed.
AUSTRALIA FIRST INNINGS 326
ENGLAND FIRST INNINGS
A COOK lbw Harris 7 (19)
M CARBERRY c Lyon b Johnson 0 (9)
J ANDERSON c Clarke b Johnson 7 (24)
I BELL c Haddin b Siddle 2 (32)
K PIETERSEN c Watson b Harris 3 (9)
G BALLANCE not out 17 (42)
B STOKES not out 23 (47)
Sundries (2nb) 2
Five wickets for 61
Fall: 6 (Carberry), 8 (Cook), 14 (Anderson), 17 (Pietersen), 23 (Bell).
Bowling: R Harris 11-4-28-2, M Johnson 9-2-19-2 (2nb), P Siddle 5-3-4-1, S Watson 3-1-5-0, N Lyon 2-1-5-0.
Batting time: 148 mins. Overs: 30.
Umpires: Aleem Dar (PAK), Marais Erasmus (RSA).