BJ Watling (52no) top-scored for the visitors with an unbeaten fifty but it was a rare day when the ball dominated in Taunton after rain delayed the start of play and then bad light brought the players off early.
When the players did take to the field after a lengthy delay, Josh Davey (2-52) struck a couple of early blows.
Scotland???s leading wicket-taker at the 2015 World Cup accounted for both Black Caps openers, Tom Latham (six) and Hamish Rutherford (37) as the visitors were reduced to 44-2.
Mitchell Santner (27) and Ross Taylor (32) recovered things with a 55-run partnership for the third wicket, before Groenewald picked up his first scalp, with Santner caught-and-bowled by the ex-Derbyshire seamer.
Two overs and 10 runs later Groenewald grabbed his second wicket, as Luke Ronchi (eight) was caught by Abdur Rehman.
Jim Allenby (2-33) then struck with a double-salvo of his own, Taylor caught behind by Alex Barrow, and Mark Craig trapped lbw for seven soon after.
That had New Zealand precariously placed at 133-6, but Doug Bracewell (20) ably supported Watling in the largest partnership of the day, the pair putting on 57 together before Bracewell became Groenewald???s third victim.
Watling reached his fifty a ball later and the New Zealanders passed 200 in what would prove to be the last over of the day, as bad light brought an end to proceedings after 59 overs.