Their good work ensured the Kiwis took a 113-run lead in to their second innings.
"They fought hard. I think we challenged them and made them work for their runs," Martin told APNZ from Zimbabwe.
"The way Dan bowls at the tail is one of his extreme kind of talents and he tends to wrap it up quite quickly and I'm glad I could help out with a couple of poles at the end there."
Zimbabwean seam bowler Kyle Jarvis, in just his third test, became Martin's 200th victim when he was caught by Ross Taylor and the veteran right-armer joined Vettori, Sir Richard Hadlee and Chris Cairns as the only other Kiwis to have achieved the milestone.
Debutant Dean Brownlie also picked up a wicket with his medium pace, while Jeetan Patel bowled 23 wicket-less overs.
As the Queens Sports Club pitch continues to slow down, the Black Caps will look to build on their lead during day four, which will put them in a good position to secure a rare test-match victory.
Their progress was halted slightly though with the late loss of Martin Guptill and Brendon McCullum as the New Zealanders finished on 28-2, 141 runs ahead.
Guptill was dismissed without scoring, which gave him the unique distinction of making a century and a duck in the same test match after his 109 in the first innings.
Former captain Stephen Fleming was the last Kiwi to register the same distinction when he made 192 and 0 against Pakistan in Hamilton in 2003.
Rookie Kane Williamson was not out on 13 with night watchman Patel unbeaten on four at the close of play.
Martin, who is known for his inability with the bat, said despite the euphoria of grabbing his 200th test scalp it didn't prompt him to request a shot at the night watchman's role.
"I've never ever been asked," he laughed.
"So I don't sort of know if that's in my resume to be night watchman at the moment."
Williamson and Taylor will be vital to the cause of the Black Caps who will want to set Zimbabwe a total of at least 300 for the fourth innings.
Scoreboard at stumps on the third day of the one-off test between Zimbabwe and New Zealand at Queens Sports Club:
New Zealand 1st Innings: 426
Zimbabwe 1st Innings
Tino Mawoyo lbw b Vettori 5
Vusi Sibanda c Taylor b Brownlie 93
Hamilton Masakadza b Bracewell 22
Brendan Taylor lbw b Vettori 50
Tatenda Taibu c Patel b Vettori 20
Malcolm Waller not out 72
Regis Chakabva run out 37
Ray Price lbw b Vettori 0
Kyle Jarvis c Taylor b Martin 6
Chris Mpofu c Williamson b Vettori 0
Njabulo Ncube b Martin 3
Extras: (3lb, 1w, 1nb) 5
TOTAL: (all out) 313
Bowling: Chris Martin 25.5-6-74-2, Doug Bracewell 23-12-51-1 (1nb, 1w), Daniel Vettori 43-13-70-5, Jeetan Patel 23-1-91-0, Dean Brownlie 4-0-13-1, Kane Williamson 2-0-9-0, Martin Guptill 1-0-2-0.
New Zealand 2nd innings
Brendon McCullum lbw b Price 11
Martin Guptill b Jarvis 0
Kane Williamson not out 13
Jeetan Patel not out 4
TOTAL: (for two wickets) 28
Bowling: Kyle Jarvis 4-0-14-1, Njabulo Ncube 2-0-12-0, Ray Price 1-0-2-1.