Shakib belted 58 off 51 balls to help the hosts to a competitive total of 228 all out. He then bamboozled the visitors with his left-arm spin to grab 4-41 as New Zealand were left stranded on 220-8 after they were set a revised target of 210 runs in 37 runs.
Brendon McCullum struck a quickfire 61 off 45 balls and gave New Zealand a strong platform after he and Jesse Ryder (21) put on 53 runs for the opening-wicket but Shakib brought Bangladesh back in contention by dismissing both batsmen before rain intervened.
New Zealand were 85-4 in 15 overs when rain stopped play for nearly an hour.
Upon resumption, Bangladesh thought they had Daniel Vettori out for nine when substitute fielder Sohrawardi Shuvo took a catch at deep square leg but Mahmudullah's full-pitched delivery was judged a no-ball.
The New Zealand captain failed to capitalize on his great escape and was out for 24, caught by Junaid Siddique off Naeem Islam. Shanan Stewart was then run out for two before Naeem removed Ross Taylor for 42 to put Bangladesh in control as the visitors floundered on 161-7.
New Zealand went into the final over needing 18 runs for victory but could only add on nine to their total as Bangladesh celebrated a rare victory and took a 1-0 lead in the five-match series.
Bangladesh were a bowler short for most of the game after skipper Mashrafe Mortaza's 27th birthday celebrations took a painful turn when he sprained his ankle in the third over of New Zealand innings.
Mortaza fell awkwardly while bowling and failed to take any further part in the game and officials said he would remain under observation for 48 hours.
