Rain arrived at Hagley Oval just after an unbeaten 49 from Sam Curran had lifted England to a competitive score off 20 overs on an unpredictable pitch.
New Zealand's batsmen never got a chance to chase, leaving just two matches to decide the series -- in Christchurch again on Monday and Auckland on Thursday.
England's batsmen struggled for fluency after being sent in, reduced to 81-5 in the 12th over when veteran opener Jos Buttler was caught in the deep for 29.
Curran injected some momentum through a flurry of boundaries over the closing stages, with 19 runs coming from the final over bowled by seamer Jacob Duffy.
England's innings was interrupted by rain, with players forced off for 30 minutes after 16.2 overs with the score at 110-5.
Captain Mitchell Santner took 1-20 off four overs of left-arm spin to be the most economical of New Zealand's six bowlers, who all took one wicket each.