New Zealand slumped from 66 for three at lunch to 147 all out with Hoggard and Andy Caddick, who dismissed three batsman in a single over, sharing the wickets.
England, who took a welcome 81-run lead after they were bowled out for 228 on the first day, were 63 for two in their second innings when bad light stopped play, losing Michael Vaughan (0) and Marcus Trescothick (33) to debutant paceman Ian Butler.
Hoggard picked up both wickets to fall in the morning session with Matthew Horne falling to a brilliant diving catch by Graham Thorpe at third slip for 14 and nightwatchman Daniel Vettori (42) edging a catch behind after some bold shots.
The burly Yorkshireman then bowled Lou Vincent for 12 before trapping Nathan Astle in front for 10 to collect his first five-wicket bag in his sixth Test.
He came back after a four-over stint from Caddick, the second of which collected three wickets, and polished off the New Zealand innings, by dismissing the hard-hitting Craig McMillan for 40 and last man Ian Butler for a duck.
New Zealand had lost three wickets with the score at 117 and it should have been four when Craig McMillan, temporarily redundant at the other end, slashed at a ball from Flintoff in the next over and was dropped by substitute fieldsman Craig White on the third man boundary.
The home side were able to get off the bogey 117 with that lapse, which was the signal to McMillan, then 16, to attempt a rescue act.
He took to Caddick in his third over and scored 15 off the over and another seven off his next. Caddick’s brief but lively spell was four overs, two maidens, 22 runs and three wickets.
ENGLAND (1st Innings) 228 (N. Hussain 106).
NEW ZEALAND (1st Innings, overnight 9-1):
M.H. Richardson lbw b Hoggard 2
M.J. Horne c Thorpe b Hoggard 14
D.L. Vettori c Foster b Hoggard 42
L. Vincent b Hoggard 12
S.P. Fleming c Giles b Caddick 12
N.J. Astle lbw b Hoggard 10
C.D. McMillan c Vaughan b Hoggard 40
C.L. Cairns c Flintoff b Caddick 0
A.C. Parore lbw b Caddick 0
C.J. Drum not out 2
I.G. Butler c Hussain b Hoggard 0
EXTRAS (LB-5, NB-8) 13
TOTAL (all out, 51.2 overs) 147
FALL OF WKTS: 1-4, 2-50, 3-65, 4-79, 5-93, 6-117, 7-117, 8-117, 9-146.
BOWLING: Caddick 18-8-50-3 (3nb); Hoggard 21.2-7-63-7 (2nb); Flintoff 12-2-29-0 (3nb).
ENGLAND (2nd Innings):
M.E. Trescothick c Vettori b Butler 33
M.P. Vaughan b Butler 0
M.A. Butcher not out 22
N. Hussain not out 6
EXTRAS (LB-1, NB-1) 2
TOTAL (for two wkts, 15.3 overs) 63
FALL OF WKTS: 1-11, 2-50.
BOWLING (to-date): Drum 4-0-16-0; Butler 7.3-0-38-2 (1nb); Cairns 4-0-8-0.—Reuters