Winners of the first test in Auckland by an innings and 49 runs, New Zealand were 256 for eight when the umpires offered Sodhi the light, still 126 runs in arrears but with the all-important draw secure.
England made the perfect start to the final day when Stuart Broad claimed wickets with the first two deliveries but the tourists were unable to winkle out the final few batsmen as the fading light cast long shadows over Hagley Oval.
Opener Tom Latham scored 83 but it was spinner Sodhi's 168-ball 56 not out that most frustrated England, who scored 307 in their first innings and 352-9 declared in the second after New Zealand's first knock of 278.
"Series victories, especially over England, don't come around that often and just to be part of this, especially when I was quite disappointed with my performance with the ball, was massive for me," Sodhi said.
"The whole time I was thinking about batting as straight as I could, they started bowling bumpers around the wicket and I found them quite hard to pick up so there were some tough periods there."
England skipper Joe Root tried every bowling option available to him and his team had their chances to take wickets throughout the day, even if none of them were clear cut.
The draw brings an end to a tour Down Under that started in October and also included a 4-0 Ashes defeat, helping extend England's run without a test win overseas to 13 matches.
The hosts resumed on 42-0 but paceman Broad removed Jeet Raval (17) with his loosener before coming up with a peach of a delivery to take the key wicket Kane Williamson for a golden duck when the New Zealand captain edged behind.
Ross Taylor blocked to prevent a hat-trick but soon became spinner Jack Leach's first test victim with a reverse sweep straight to Alastair Cook at short backward square, the former skipper departing for 13.
Henry Nicholls also made 13 before he became paceman James Anderson's 531st test victim, miscuing a drive that took an edge into the hands of Cook in the slip cordon.BJ Watling scored a battling 19 before getting across the crease to flick Mark Wood to Anderson at backward square before Leach got his second wicket when Latham top-edged a sweep to be caught by James Vince.
Sodhi put on 47 runs for the seventh wicket with Colin de Grandhomme and New Zealand looked in real trouble when the all-rounder pulled a Wood bouncer to Leach at fine leg for 45.
Neil Wagner came out and joined Sodhi at the crease, however, and the pair batted through 31 overs until the paceman was dismissed after a 103-ball knock of seven in what turned out to be the last action of the series.
First Published: April 3, 2018, 12:12 PM IST