But just as the tourists appeared to be heading towards a second straight defeat in the five-match series, fast bowler Peter Siddle led a spirited fightback with the wickets of Alastair Cook (8), Jonathan Trott (0) and Kevin Pietersen (5) as England was reduced to 31-3 at stumps. Siddle was 3-4 from five overs.
Joe Root was 18 not out and nightwatchman Tim Bresnan was yet to score. Root had also enjoyed some fortune when he edged Shane Watson between wicketkeeper Brad Haddin and first slip Michael Clarke when on 8. Seemingly, Haddin should have attempted a routine catch.
England, which racked up 361 in its first innings, still led by 264 runs because of its significant first innings lead. Australia lost the first test by 14 runs in Nottingham.
The pitch offered considerable turn for Swann but in hot and sunny weather on a dry and flat surface, conditions still favoured batting despite 16 wickets falling in the day, as celebrities such as Mick Jagger, Russell Crowe, David Cameron and Elizabeth Hurley watched from the sidelines.
"I'm not going to count my chickens as Australia will fight as we saw with those three late wickets," Swann said. "I really don't know why 16 wickets fell in the day. It was a mixture of some good bowling and some outrageous fortune.
"From a personal viewpoint I was already on the honours board for five wickets I took against Pakistan (in 2010) but that game was tainted, so it's pleasing to get up there again here."
Cook and Trott each played on to Siddle, while the unpredictable Pietersen played a casual, loose drive to Chris Rogers at point just 20 minutes from the close to give the Australians some cheer at the end of what had been a bitterly disappointing day for them.
"It was a bad day, we didn't bat well full stop," Australia coach Darren Lehmann said. "The big thing for us is making more runs - it's that simple. The top order failed again and we need to make sure we are learning from our mistakes.
"It was more one-day batting than test batting. Eight of the 10 were self-inflicted. We have to get it right quickly."
However, he still believed Australia was in contention.
"You've always got a chance. It's a funny game, cricket," he said. "I've seen big totals chased down and it is a good wicket. It's certainly not a 128 wicket."
Australia's demise began with the fall of Watson for a top score 30, to the last ball before lunch. He was lbw to Bresnan and wasted one of his team's two reviews in the process. Lehmann said it was Rogers' idea to use the review.
Rogers, playing on his home ground and where he is captain of county team Middlesex, was lbw to Swann for 15, though in farcical circumstances. Swann bowled an ugly waist-high full-toss which the left-hander tried to pull towards the Tavern Stand only to miss his connection and be struck in the mid-rift.
Umpire Marais Erasmus ruled the ball was dipping sufficiently to hit the stumps. Rogers opted not to utilise his team's remaining review. If he had, he would have been reprieved as replays showed the ball missing leg stump.
"I'm not sure there has been a worse piece of cricket in test history," Swann joked afterwards. "I'm sure he was as embarrassed as I was."
That was 50 for two, which became 53 for three when Phil Hughes attempted a smear through cover at a wide Bresnan delivery, only to be given caught behind for 1.
He immediately reviewed his dismissal but third umpire Tony Hill upheld the original decision through lack of evidence to the contrary - there was no obvious mark on hot-spot but there was a slight noise.
Usman Khawaja was dropped on 7 by Trott at slip off Swann, who had his revenge when the left-hander irresponsibly tried to hit him over long-off only to find Pietersen at mid-off. That was 69 for four.
Steve Smith prodded a Swann off-break to Ian Bell at short-leg to make it 86 for five, while Australia captain and the team's talisman Clarke was trapped lbw by Stuart Broad for 28. It was 96 for seven with the needless run out of Ashton Agar for 2.
Siddle, Haddin and Ryan Harris followed after tea, with the latter hitting Swann to Pietersen at mid-on to hand the spinner his five-wicket milestone.
An aggressive last-wicket partnership of 48 earlier boosted England's first innings total. Broad (33) and Swann (28 not out) clubbed the precious runs in just 40 deliveries. Their effort undermined the excellent bowling display from Harris, who claimed five for 72 to secure his name on the famous Lord's honours board.
Bell hit 109 for the second straight match after England won the toss on Thursday. He steered his team out of early trouble when it had crashed to 28 for three.