England lost Tim Bresnan to the first ball of the day to slip to 289 for eight but Swann (28 not out) and Stuart Broad (33) helped them recover to 361 all out in an aggressive last-wicket stand worth 48.
The hosts then carried that momentum into Australia's first innings, where Swann's five for 44 helped England skittle the tourists for just 128.
Australia hit back again the final session with Peter Siddle reducing England to 31 for three by the close, but with a lead of 264 Alastair Cook's side are still in the box seat.
Swann agreed it had been a great day for England, telling Sky Sports: "It was (a great day). Obviously losing a wicket first ball wasn't ideal but I think we bounced back well with the bat, and then to bowl Australia out for 130 or whatever, we'd have bitten anyone's hand off at the start of the day if they'd offered us that."
Regarding his key partnership with Broad, Swann said: "We talked about just getting as many as possible on this pitch. We thought it was a pitch that was much more of a 450 pitch, so we were a bit below par and talked about getting as many as possible. I thought I was too defensive at Trent Bridge, I was trying to bat like a proper batsman rather than a tail-end clubber so today I just tried to club it a little bit."
Swann's opening wicket in Australia's response was a bizarre one with the spinner trapping Chris Rogers lbw but via a box-high full-toss.
Swann admitted it was not a delivery he was particularly proud of, saying: "It's quite simply the worst ball I've bowed, it just slipped out of my hand. It was truly awful cricket. I was a bit embarrassed but I'm sure Chris Rogers was more embarrassed."
Australia coach Darren Lehmann praised his side's bowlers for the way they hit back late on as Cook, Jonathan Trott and Kevin Pietersen all fell cheaply.
He said: "We didn't bat well enough as a side, we know that. We need to bowl well and keep us in the game tomorrow, be really aggressive like we were tonight. I was really impressed with the bowlers especially after not having much rest. We're gonna chase a large total but we're gonna have to chase it."