A 103-ball stay for Neil Wagner also proved pivotal, as the Black Caps claimed a 1-0 series victory.
England end the winter without a single win in Test cricket, having also lost 4-0 in The Ashes, making it 13 overseas matches since their last triumph.
After a dream start for the tourists, which saw Stuart Broad dismiss Jeet Raval for 19 and Kane Williamson for a duck inside the first two deliveries, they were well positioned to end that barren run.
Colin de Grandhomme went for 45 runs with 27 overs remaining, with New Zealand on 219-7 at that point, yet Sodhi and Wagner refused to buckle.
The two men held on to ensure that the Kiwis claimed a first series win over England on home soil since 1983-84.