The pair have ensured Bangladesh are dictating terms at Wellington's Basin Reserve after being sent into bat in what appeared to be prime bowling conditions.
Shakib was on 126 and Mushfiqur on 112 with their 231-run partnership a Bangladesh record against New Zealand, surpassing the previous best 161 set by Tamim Iqbal, in his Test debut, and Junaid Siddique nine years ago.
The only wicket lost in the first two sessions of the second day was day one rock Mominul Haque who was unable to add to his overnight 64 before he was caught behind off Tim Southee.
New Zealand wasted a review after an appeal against Shakib on 87 was turned down and the replays showed the ball had clipped the thigh pad.
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Shakib had survived one life before stumps on day one when he was dropped by Mitchell Santner on four.
He progressed steadily on with 18 boundaries in his 168-ball innings and brought up his century turning Neil Wagner to fine leg.
Mushfiqur's hundred came from a boundary off Southee, the 16th four of his innings.
Even when New Zealand took the new ball as soon as it became available, the Bangladesh pair proved unflappable and cracked another 106 runs in the 21 overs before tea.
Their enterprise with the bat left Southee with figures of two for 132 off 27 overs while Trent Boult has one for 106 off 25.
On a bowl-first wicket, Bangladesh's 391-4 is the best performance in five Tests at the Basin Reserve since England managed 465 in 2013.