Pacer Naseem Shah (3-58) dismissed Conway on the last ball of the 30th over to lift New Zealand from a 181-run partnership for the second wicket between Conway and Williamson.
Conway hit 13 fours and a six in his second ODI century off 92 balls.
Nawaz then took three wickets by dismissing both Daryl Mitchell and Tom Latham cheaply in one over and clean bowled Williamson.
Williamson, who was dismissed for 53 and 54 off Wasim, hit 10 fours in his 100-ball innings.
Mitchell Santner, one of only three New Zealand batsmen to reach double figures, was the last to be dismissed for 37.