Peter Siddle then gave Australia hope with a return of three wickets for four runs in five overs.
Big guns fallEngland captain Alastair Cook and Jonathan Trott both played on before Kevin Pietersen loosely carved the paceman to Chris Rogers at point.
Although England were 31 for three in their second innings at stumps, they still led by 264 runs.
Joe Root, missed on eight when wicketkeeper Brad Haddin didn’t go for a chance, was 18 not out and nightwatchman Tim Bresnan unbeaten on nought.
Swann was the first England spinner to take five wickets in an innings of a Lord’s Ashes Test since Hedley Verity (seven for 61 and eight for 43) managed the feat twice in 1934.
How Australia’s top-order performed was always likely to be a key factor in whether they could regain the Ashes and, unlike the first Test, the tail was unable to cover up the failings of the specialist batsmen.
Australia were all out inside 54 overs and, after opener Shane Watson was out for an innings top score of 30, they lost 10 wickets for 86 runs.
Bresnan took two wickets to spark an initial collapse that saw Australia’s 42 without loss transformed into 53 for three wickets.