New Zealand compiled 164 for nine and England opener Darren Maddy, who took two wickets, scored a half century but his side ran out of overs to finish on 159 for eight.
McMillan hit three fours and four sixes, adding 60 runs for the fifth wicket with Scott Styris (42) after the side had slumped to 31 for four in the sixth over.
Maddy, who took two wickets for six with his medium pace, broke the partnership in the 13th over with a direct hit from mid-wicket at the non-striker's end to run out Styris.
Maddy's productive over helped England fight back at the end of the innings with three wickets falling for 11 runs in eight balls.
Batsman Vikram Solanki kept wicket for England after Matt Prior was ruled out after breaking his thumb in practice on Monday.
Maddy and Solanki (25) returned to open England's innings with a bustling stand of 62 but the rest of the order failed and New Zealand's win was assured when they took three wickets in the 19th over.