Swann contributed 28 not out, including five fours, to a last-wicket stand of 48 to get England up to 361 in their first innings in the morning session on day two.
He did not take the field for the start of Australia's reply as he required treatment after being hit on the right forearm while batting, close to the spot he injured in similar fashion during the pre-series warm-up win over Essex.
But he returned to the field soon enough and took centre stage as Australia's batting collapsed during the afternoon session.
The first of his five wickets was a gift. Chris Rogers was lbw after missing a full toss that hit him just below the waist, a delivery that 'Hawkeye' showed was missing leg stump.
But thereafter he tormented Australia's fragile line-up, finishing with 5-44 to get his name on the Lord's honours board for the second time.
His efforts saw Australia all out for 128, giving England a first-innings lead of 233 which they extended to 264 by reaching 31-3 in their second innings at stumps.