Even though the entire opening day of the First Test was lost due to rain, New Zealand looked set for victory throughout most of the last four days.
The Black Caps bowled out England for a paltry 167 in just 55 overs on the second day to take advantage of the Test thanks to 4-42 from Neil Wagner and 4-43 from Bruce Martin.
Debutant opener Hamish Rutherford, the son of former New Zealand captain Ken, then put the Black Caps in a dominant position as he went on to make a brilliant 171 from 217 balls with 22 fours and three sixes.
With Peter Fulton adding 55, Brendon McCullum 74 and Martin 41, New Zealand went on to amass a huge 9(dec)-460 before sending England into bat for a second time with the Black Caps 293 runs in front.
However, this time England was going to make a better fist of their time at the crease and with the pitch flattening out and offering less and less for the bowlers, opening pair Cook and Compton fully cashed in.
Cook added yet another century to his blossoming career as captain of England while his opening partner Compton reached triple-figures for the first time in five-match Test career.
The pair put on an opening partnership of 231 to get England to within 62 of forcing New Zealand to bat again before Cook fell for 116 late on the fourth day.
Fast bowler Finn then came to the wicket as nightwatchman and he survived until stumps without scoring with Compton not out on 102 overnight with England 1-234.
With only New Zealand a chance to push for victory on the final day, England's task was simply to bat out the day and hold on for a draw.
Even though Compton fell early on Sunday for 117 when trapped LBW by Wagner with England 2-265, occupation of the crease then wasn’t a major problem for the rest of the day with Finn leading the way.
Finn played an innings reminiscent of some that Jason Gillespie had for Australia and by the time he was out with England's score 5-386 late on the final day, he had more than done his job of ensuring his team could not lose.
In all, Finn made 56 from 203 balls while spending almost five hours at the crease.
Finn looked the most assured of all England batsmen trying to survive with Jonathan Trott out for 52, Kevin Pietersen for 12 and Joe Root run out for 23. Ian Bell finished not out on 26 and Matt Prior 23 as England finished on 6-421 with a lead of 128 when the draw was called.
Wagner took 3-141 in the second innings for New Zealand with Trent Boult and Martin claiming a wicket apiece.
New Zealand captain Brendon McCullum was delighted with the effort of his team and realistic enough to know that the Black Caps likely would have won had the first day not been lost to rain.
"I thought that from the moment we stepped on the field to when we stepped off it we showed the heart and characteristics we want to be known for. There were some outstanding debuts and Hamish Rutherford's effort was something special," McCullum said.
"Everyone at the ground and everyone in this team will remember that for a long time. Bruce Martin as well did a good job and the bowler's effort over the last two days was phenomenal, and we never gave up belief that we could get the job done but we weren’t quite able to finish it off.
"Another day of Test cricket would have been phenomenal. When you lose that first day I guess you have to work out how you can fit such a good game into four days, and unfortunately we weren’t quite able to.
"I thought it was a great game for us and England showed some fighting characteristics with the bat as well in that second innings. Overall it was a great start to the Test series."
The Second Test starts in Wellington on Thursday.