Having kept England to 361 all out, less than they had fancied after winning the toss on Thursday and batting first, Australia capitulated for just 128 - a 233-run deficit.
Swann played a big hand in that, claiming five for 44 and applying constant pressure on a flimsy line-up.
But Peter Siddle kept England honest as he took all the wickets in England's 31 for three, a nervy effort but one that nevertheless leaves the home side 264 ahead with seven wickets in hand.
Swann urged caution but was clearly a satisfied man at the close of play.
"I'm not going to count my chickens, there's still three days to go," said Swann, whose haul lifted him into England's top 10 all-time wicket-takers with 231.
"The Australians aren't just going to lie down and take it.
"They bounced back really well tonight [Friday] with those three wickets.
"That will have buoyed them and forced us to regroup in the morning.
"We thought it was about a 400 pitch so to get 361 we reluctantly accepted, but then to get Australia out for so far behind that...we'd have bitten your arm off at the start of the day."
England followed a tried and tested method of not enforcing the follow-on when it was available and instead plan to unleash Swann on Australia in the final innings.
He saw enough in Friday to believe there will be plenty in the pitch for him at his next visit, but wants the batsmen to lay a lengthy foundation before he tries his luck.
"There is a bit of rough to work with but the main part of the pitch I care about is the benign bit in the middle and that needs another day baking under the sun.
"It needs to start breaking up and turning a lot more before I start waving about grandiose comments about us winning this game."
The anomaly in Swann's contribution with the ball came when a wild full toss slipped out of his hand and was inexplicably missed by Chris Rogers.
He found himself given lbw, though Hawk-Eye technology showed the ball to be missing the stumps.
"I'm not sure there's been a worse piece of cricket in Test history," laughed Swann.
"I'm sure he (Rogers) is as embarrassed as I was. It completely slipped out of my hand; it did well to be going anywhere near the wicket."
Australia coach Darren Lehmann was the man put forward to make the case for his side but he pulled no punches.
Having made it clear before the struggling top order must do more he was left making familiar calls for improvement.
"It was a bad day," he said.
"We didn't bat well, full stop. The big thing for us is making more runs. It's simple.
"The top order failed again, and we need to make sure we're actually learning from our mistakes. We probably haven't done that from the first innings at Nottingham to the first one here.
"We've shown glimpses. But we've got to bat better - it was more one-day batting than Test match batting.
"We have to bat a lot longer than 55 overs...the top six have got to start making hundreds.
"Our shot selection was poor today [Friday]. Eight out of the 10 were self-inflicted."
Despite his clear dissatisfaction, one of Lehmann's greatest qualities is his never-say-die attitude.
And he proved that was alive and kicking, adding: "You've always got a chance. It's a funny game, cricket - I've seen big totals chased down, and it is a good wicket.
"It's certainly not a 128 wicket. The key is we have to bowl them out tomorrow morning [Saturday] to get us in the game."