Despite the best efforts of England nightwatchman Steven Finn and New Zealand quick Neil Wagner on the final day, an outright result was never more than a remote possibility on the unresponsive wicket.
New Zealand saw a glimmer of hope in the first three overs after tea when Finn was eventually removed after 203 minutes at the crease for 56 and Root quickly followed without scoring.
But Ian Bell, with an unbeaten 26, and Matt Prior not out 23 carried England through to stumps without further loss and saw off the third new ball in the process.
Although a draw, New Zealand captain Brendon McCullum saw it as a morale-boosting performance for his side who dominated the early stages of the Test against the world's second-ranked side.
"We never gave up the belief that we could get the job done but we weren't quite able to finish off," he said, rueing the time lost through rain.
"Another day of Test cricket would have been phenomenal. You lose that first day and you have to try and work out how to congest such a good game into four days. Unfortunately we weren't able to."
England resumed the final day at 234 for one and added 31 before Nick Compton fell for 117, trapped leg before wicket by a swinging delivery from Wagner.
Compton's maiden Test century and his 231-run opening stand with Alastair Cook (116) when England were fighting to save the Test may well have secured his international career, which had been under the microscope after his previous nine innings had produced a best score of only 57.
Wagner, a late inclusion in the side when Doug Bracewell cut his foot, staked a strong claim to be retained for the second Test after finishing with figures of three for 141 to go with his four wicket bag in the first innings.
In the session between lunch and tea the left-arm seamer claimed the wickets of Jonathan Trott, caught and bowled for 52, and Kevin Pietersen who was caught behind for 12.
As the senior batsmen came and went, nightwatchman Finn doggedly pressed on to his maiden half-century, frustrating the New Zealand bowlers as he played a straight bat to anything heading towards the stumps.
He survived two tough chances, edging the ball towards the slip cordon, and his 203 minutes at the crease included a 72-minute period when he faced 50 dot balls before advancing from 53 to 54.
But having refrained from anything flashy for more than two sessions Finn was undone immediately after tea when he attempted to play across the line against Bruce Martin and was deemed leg before wicket.
Joe Root was briefly in the middle when he was called through for an unnecessary single by Bell and was run out without scoring on a direct hit from Tim Southee.
Bell and Prior then steered England safely through to stumps which was called with a minimum 15 overs remaining in the day.
Although Wagner was the principal wicket taker for New Zealand, Trent Boult was the most economical bowler with one for 49 from 35 overs and Martin bowled 44 overs to take one for 90.