Finn went 49 balls without a single scoring shot at one stage of his near five-hour 56, but England could nonetheless be grateful that he made the move up from number nine to three so seamless with his maiden half-century in any professional cricket.
After Saturday's epic opening stand of 231 between centurions Alastair Cook (116) and Nick Compton (117), England began a sunny final day with strong prospects of ensuring a draw at the start of this three-match series.
But they might reasonably have expected their main contributor to be any one of seven other contenders with substantially better batting pedigrees than fast bowler Finn, with his previous highest first-class score of 32. He could muster only five fours from 203 balls, having batted throughout two sessions today before finally falling when he missed a sweep at slow left-armer Bruce Martin to be lbw immediately after tea.
Finn's departure induced one final wobble, Joe Root run out for a duck an over later when Tim Southee's dive and direct hit from cover was too quick for the young Yorkshireman as he answered Ian Bell's call for a single. But in Bell and Matt Prior, England still had two frontline batsmen in reserve - and their unbroken stand of 31 against the third new ball took their team to the safety of 421 for six before New Zealand agreed to call time 128 in arrears.
Compton's was the only departure of a sunny morning, to Neil Wagner (three for 141). But Jonathan Trott (52) and Kevin Pietersen also went to the left-arm seamer as England made 53 for two from 28 overs in the middle session and the onus fell increasingly on Finn to keep the Kiwis at bay.
Compton augmented his maiden hundred by just 15 runs before falling lbw; Trott shared a third-wicket stand of 90 with Finn but went caught-and-bowled, and then Wagner got Pietersen for the second time in the match following his first-innings golden duck. Finn, meanwhile, not only improved his Test-best twice in the same match but dug in for a cussed central role.
Compton reopened his account in the fifth over of the day with a trademark extra-cover drive for four off Southee, but was to be the only casualty before lunch - falling over slightly in defence as Wagner found just a hint of inswing. His 310-ball vigil was over after almost seven hours at the crease, mostly in company with Cook. Thanks to them, England's remaining batsmen could be encouraged that survival ought to be routinely viable on a pitch showing no signs of deterioration.
Trott was fluent on his way to a 78-ball 50, which he completed with his eighth four - in his favourite direction past straight midwicket off Southee. But the return of Wagner undid him, extra bounce inducing a return catch in startled back-foot defence, and Pietersen never looked comfortable in his short stay before he got a faint inside-edge behind. Finn's stoic presence verged on the strokeless after he reached his 50, as he came to terms with his new responsibilities, especially once Trott was gone. His durability, though, in the second-longest innings by any English nightwatchman down the years was nonetheless the main reason the tourists managed to steer clear of further anxiety.
They can therefore head to Wellington tomorrow, for next week's second Test, relieved that their hapless first-innings collapse to 167 all out did not cost them as dearly as it might in this rain-shortened match.