New Zealand, following on, were 45 for two at tea on the third day - still 196 runs behind England's first innings 364 - in a match they had to win to end the series all square at 1-1.
Broad, in front of a crowd including his father Chris, the former England opening batsman, then backed up his double strike by having Aaron Redmond caught behind to leave New Zealand 21 for one in their second innings.
And his Nottinghamshire colleague Ryan Sidebottom, the third member of England's pace trio, piled the pressure on the tourists when opener Jamie How, dropped on 12, was caught at third slip by Alastair Cook for 19.
Brendon McCullum was 16 not out and Ross Taylor eight not out.
New Zealand, who resumed on their overnight first innings score of 96 for six, were dismissed for 123 - 42 short of the follow-on avoidance total of 165.
They lost their last three first innings wickets for no runs after rain meant there was no play before lunch.
Lancashire quick Anderson's final figures of seven for 43 in 21.3 overs were the 25-year-old's best of his first-class career.
But it was left-armer Sidebottom who struck first Saturday and so ended any hopes Anderson had of becoming the third man, and first pace bowler, after England off-spinner Jim Laker and India leg-spinner Anil Kumble, to take all 10 wickets in a Test innings.
Sidebottom induced New Zealand captain Daniel Vettori to drive without moving his feet and Andrew Strauss made no mistake with the first slip catch.
While Anderson initially struggled to control the extravagant movement on offer in overcast conditions ideal for swing bowlers, Broad needed just three balls Saturday to have Kyle Mills caught at backward point by Kevin Pietersen.
Two balls later, Broad, who'd already had a match to remember with a Test-best 64, produced a superb outswinger which pitched on middle and hit off-stump to bowl Iain O'Brien for nought.
Anderson though had the last word when debutant wicket-keeper Gareth Hopkins was lbw for 15.