England at lunch was on 341/8 with Broad on a career-best 49 not out and Ryan Sidebottom on three. Regular number 11 batsman Anderson, brought in as a nightwatchman on Thursday evening ahead of Sidebottom, made 28.
England tail-enders frustrated clueless New Zealanders for over a hour-and-half of the first session before Anderson was dismissed.
The hosts need only to avoid defeat in the match to win the series after drawing at Lord's and winning the second Test at Old Trafford by six wickets.
The Kiwis did have their chances as Broad was dropped on 21 by second slip Brendon McCullum, a wicketkeeper playing solely as a batsman because of a back injury, off Chris Martin when the score was 279 for seven.
The six-foot-five left-hander Broad then raised England's 300 with a square drive for four off the luckless Martin.
Iain O'Brien, New Zealand's most successful bowler on day one with four wickets, was introduced after an hour but Anderson's perfectly executed cover drive for four demonstrated his growing confidence as the fifty partnership came up.
Anderson swept New Zealand skipper Daniel Vettori for four through midwicket next over to register his highest Test score, beating the 21 not out he made against South Africa in 2003.
Broad further strengthened England's position with two handsome back foot drives for four off O'Brien - the first punched through mid-off and the second cut through the covers and the latter also gave him his highest Test score, beating the 42 he made in Napier in March.
Broad was given a third life when on 46 as his thick edge off Jacob Oram was dropped by Aaron Redmond at gully, diving to his right and failing to hold a difficult chance.
But in the same over Anderson edged to wicketkeeper Gareth Hopkins, missing the opportunity to pass his highest first-class score of 37 not out.
Broad was stranded on 49 for 22 balls before the lunch interval.
Brief Scores (at lunch, D-2):
England Ist innings 341/8 (Pietersen 115, Tim Ambrose 67, Staurt Broad 49 n o, Strauss 37, Anderson 28; Iain O'Brien 4/74, Kyle Mills 3/76, Oram 1/35) Vs New Zealand.