Shakib returned 2-1 as New Zealand struggled to reply Bangladesh's first innings total of 282.
Peter Fulton scored 14 and Hamish Rutherford made 13 in a 31-run opening stand before Shakib struck with the last ball of his first over.
He had Rutherford caught at short leg to end the 13th over, then trapped Fulton lbw with a quicker delivery in the second ball of his second over at Mirpur's Sher-e-Bangla National Stadium.
Wagner struck early in overcast conditions, taking out Bangladesh skipper Mushfiqur Rahim on 18, after he added just four runs to his overnight total. Wagner also dismissed first test centurymaker Sohag Gazi (14) and Rubel Hossain (4) to pay back selectors who favored him at the expense of left-arm spinner Bruce Martin.
Legspinner Sodhi took advantage of some turn and bounce in the pitch and claimed the wickets of Nasir Hossain (19) to a ball that spun sharply and Abdur Razzak (13).
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