New Zealand were 173 for two at tea in reply to England's first innings 345, a deficit of 216 runs, after Martin Guptill (70) and Tom Latham (59) put on 148 for the first wicket.
Kane Williamson was 11 not and Ross Taylor seven not out.
Just when it seemed the openers would bat through to tea, England took two wickets for no runs in three balls.
Off-spinner Moeen Ali succeeded where England's quicks had failed by having Latham lbw as the left-hander tried to turn the ball legside.
More From This Section
Latham's innings was all the more impressive after he found himself keeping wicket for 75 overs while England batted after first-choice gloveman BJ Watling went off injured on Thursday.
Next over, 148 for one became 148 for two when Guptill carelessly drove a Stuart Broad outswinger low to Gary Ballance at cover.
Guptill, one of the stars of New Zealand's run to the World Cup final but playing his first Test in two years, trudged off slowly having put himself in position to press on for a coveted hundred at Lord's.
Then, with both new batsmen on nought, Williamson called for a reckless single which would have seen Taylor run out had bowler Broad's underarm throw hit the stumps at the striker's end.
England might, however, have seen the back of both openers when they were each in the 20s.
Guptill was on 24 when he edged debutant fast bowler Mark Wood to England captain Alastair Cook at first slip.
But would have been the Durham paceman's first Test wicket to be rubbed out when an umpire review to check for a no-ball showed he'd overstepped the crease by a fraction.
England were often ragged in the field during Friday's second session, with one Broad bouncer sailing over wicket-keeper Jos Buttler's head for four byes.