The 30-year-old late bloomer was a surprise inclusion in the New Zealand side, but fully justified his selection, swinging and seaming medium pace deliveries which the Pakistan batsmen found difficult to handle.
Only seven other New Zealand bowlers have taken five or more wickets on debut with the previous best figures belonging to Tim Southee at five for 55.
The previous record bowling figures on debut were Alex Moir's six for 155 against England 65 years ago.
After a washout on Thursday at Hagley Oval in Christchurch, the arrival of the sun and the promise of a full day's cricket on Friday signalled the late arrival of Harare-born De Grandhomme on the international scene.
De Grandhomme broke through the Pakistan top order before lunch and, in the first over after play resumed, dismissed Asad Shafiq, who had been rebuilding the innings with Misbahul Haq. He then mopped up the tail just before tea.
The Pakistan openers Sami Aslam and Azhar Ali had made a promising start after being sent in to bat, progressing to 31 and seeing off New Zealand's established new-ball pair Southee and Trent Boult in the first hour.
But their innings began to unravel when all-rounder De Grandhomme came on as a surprise first-change bowler. He removed Azhar (15) in his third over and then accounted for Babar Azam (seven) and Younus Khan (two) in quick succession.
Southee, bowling with more discipline in his second spell, had Aslam caught by New Zealand's second debutant Jeet Raval for 15 and Pakistan went to lunch at 88-4.
Four balls after lunch, De Grandhomme bagged his fourth wicket as he tempted Asad Shafiq to poke at a full delivery that was swinging away and Raval snared his third catch at second slip.
It left Pakistan again looking to their veteran skipper Misbah to lead them out of trouble.
The 42-year-old, playing a record 50th Test as Pakistan captain, was the epitome of patience in reaching 31 off 108 deliveries before he slashed at a Boult flyer and was caught by Kane Williamson.
A fragile bottom order put up little resistance as Southee disposed of Sarfraz Ahmed (seven) and De Grandhomme removed Sohail Khan (nine) and Rahat Ali without scoring.
In addition to De Grandhomme's 6-41, Southee took two for 20 while Boult had figures of two for 39.
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