The off-spinner missed three Tests against the same opposition earlier this year after undergoing surgery on a troublesome elbow injury and was only required to bowl eight overs in the series opener at Lord's as the seam attack excelled. But when he was called on at Headingley he produced a superb spell to help dismiss the tourists for just 174.
"It's only the third time I've bowled since the operation. Obviously with having the operation, and with such a big summer ahead, it's important to get wickets under your belt," he said. "I was optimistic I'd be able to get back playing and be able to perform but whether you'll have the rhythm and the spin in the fingers you're never sure."
He added: "So I'm delighted it seems to be coming out nicely. It feels just like it did 18 months ago again and that's very encouraging for me."
He finished with four for 42, starting with two devastating overs that included the scalps of Dean Brownlie, Martin Guptill and Kane Williamson.
The follow-on margin was reduced from 200 ahead to 150 due to the day-one washout, meaning England could have enforced it with their 180-run first innings lead.
Instead they batted themselves and the sight of Nick Compton registering a fourth successive failure in the series, this time managing just seven runs in a stodgy 45-ball stay, was the only real blight on the day.
It was his last chance to impress before the Ashes, but Swann insists Compton retains the confidence of his team-mates.
"It's a shame when someone misses out and Compo's obviously had a fairly low-scoring game. He hasn't hit the standards he expects of himself but we know what a magnificent player he is.
"He played with aplomb in the winter and he has support of everyone in the dressing room support. I bowl at him in the nets so I know how good he is and he'll be scoring heavily in no time."