Anderson, fresh from becoming the fourth Englishman to reach 300 Test wickets yesterday, was again the catalyst on the third morning as the Kiwis lost their last six wickets for 52 runs.
Then, with a 25-run lead in the bank, England recovered from the loss of both openers with the total stuck on 36 to reach a teatime 91 for two in their second innings.
Alastair Cook, who had survived a DRS process for caught-behind on nought before lunch to Trent Boult, fell to the left-armer anyway when Dean Brownlie took an outstanding catch diving to his left at third slip.
Nick Compton was then bowled through the gate by a Neil Wagner inswinger, but Jonathan Trott and Joe Root closed out the afternoon session in an unbroken stand - England's first of 50 or more in the match.
Stuart Broad made the first breakthrough, with the important wicket of Brendon McCullum, and then Steven Finn, who recorded figures of four for 63, saw off the tail.
McCullum edged an attempted drive at Broad to Matt Prior. The Kiwi captain reviewed Steve Davis' decision on DRS, but to no avail.
Kane Williamson had completed a painstaking and valuable half-century, but eventually fell to Anderson when Aleem Dar detected an edge behind and Tim Southee tried typically different tactics, targeting Finn for three successive off-side fours in the tall seamer's first over only to then offer a catch into the off side.
Anderson completed his five-wicket haul by making short work of Bruce Martin, gone for a third-ball duck to a perfect delivery which shaped in and held up down the slope off the seam to beat the forward defence and hit the top of off stump.
But it was Finn who took the last two wickets in the same over, BJ Watling wafting another edge behind and last man Trent Boult fencing a simple catch to gully.