Ajmal took 4-30, his fourth four-wicket haul in Twenty20 cricket, as Pakistan restricted New Zealand to 164-9 after setting them a daunting 178-run target on the back of a brilliant career best 56 by Nasir Jamshed at Pallekele stadium.
New Zealand gave Pakistan a scare in the final five overs when they needed an improbable 70 runs, with captain Ross Taylor hitting three boundaries off Umar Gul's penultimate over before he was run out for an 11-ball 26.
Ajmal was the difference between the two sides as Pakistan unleashed its spinners, while Kiwi opener Rob Nicol (33) and Brendon McCullum (32) made major contributions to the New Zealander's reply.
Pakistan play Bangladesh in the final match on Tuesday in the group from which the top two teams will qualify for the Super Eights.
Brendon McCullum, who made the highest T20 score of 123 in his team's 59-run win over Bangladesh, hit four boundaries and a six but was finally bowled in the 16th over by Gul to almost end New Zealand's hopes.
Earlier Jamshed made a 35-ball 56 and added 76 for the second wicket with skipper Mohammad Hafeez (43).
Jamshed hit two boundaries and four sixes as Pakistan plundered 92 off the first ten overs. Hafeez hit two fours and two sixes off 38 balls.
Imran Nazir made 25 with five boundaries.
Jamshed was aggressive from the start, smashing paceman Adam Milne for a six before hitting two off spinner Nathan McCullum's successive overs. He reached his maiden fifty off just 27 balls, improving on his previous best of 45 he made against Australia in Dubai last month.
New Zealand reined them in in the middle overs, claiming three wickets for just 11 runs including that of Jamshed caught in the outfield off Daniel Vettori.
Umar Akmal scored 23 with three boundaries and a six.
New Zealand were uncharacteristically sloppy in the field, with Taylor dropping Hafeez on nought in Kyle Mills's first over while Nicol failed to hold on to a head-high Jamshed hook off the same bowler which went for six. – Sapa-AFP