The Black Caps, set a D/L target of 216 in 33 overs, were 126-6 in 25 overs when bad light ended play. The tourists should have been 162 at that stage to win.
Sri Lanka had made 211-8 from 33 overs after the start was delayed by 90 minutes due to bad weather.
New Zealand had won the second game in Hambantota on Tuesday after the first match was rained off.
New Zealand will round off their short two-week tour with two Twenty20 internationals in Pallekele on November 19 and 21.