At the close, England were 116 for one in their second innings -- a lead of 296 runs -- after Swann starred in New Zealand's second straight batting collapse.
England captain Alastair Cook, who opted against enforcing the follow-on, was 88 not out and Jonathan Trott 11 not out.
Earlier, fast bowler Steven Finn took the first three New Zealand wickets to fall before Swann followed up with four for 42 in nine overs.
Swann, England's premier spin bowler and likely to be a key figure in the defence of the Ashes starting in July, missed the recent tour of New Zealand because of an elbow injury and this was only his second Test since surgery on the troublesome joint.
That left the tourists 180 runs behind, with New Zealand needing to be within 150 of England's first innings to deny Cook the follow-on choice after Friday's first day washout.
New Zealand's total may not have been as bad as their second innings 68 in England's 170-run win in the first of this two-match series at Lord's last week, but it was again well short of what was required.
But then Peter Fulton, trying to turn Finn legside, got a leading edge and was caught and bowled.
Then a superb over to Hamish Rutherford, the other opening batsman, saw Finn beat the left-hander three times in a row outside off-stump.
Rutherford did not heed the warnings and a loose drive saw him edge Finn to Ian Bell in the gully for 27.
Ross Taylor fell for six after playing on to a fast Finn delivery that cramped him for room.
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
