Compton (117) augmented his maiden hundred by 15 runs on a sunny final morning before he was lbw to Neil Wagner in the tourists' 275 for two.
Nightwatchman Steven Finn made the early running and is on course to improve his career-best twice in the same match, after his first-innings 20.
Compton had to wait until the fifth over before he could add to his overnight 102, but did so in style with a trademark extra-cover drive for four off Tim Southee.
He was to be the only casualty before mid-session drinks, though, falling over slightly in front-foot defence as left-armer Wagner found just a hint of inswing.
Compton's 310-ball vigil was therefore over after almost seven hours at the crease, mostly in company with his captain Alastair Cook in an opening stand of 231 yesterday. Thanks almost entirely to them, England's prospects of closing out a stalemate on a pitch showing no signs of deterioration were becoming ever more obvious.
That, of course, would be a highly favourable outcome after their first-innings collapse to 167 all out.
- Sports & Recreation