The tourists scrambled to 256 for nine and a lead of 333 after their hosts had declared behind on 349 for seven.
But without counter-attacking innings from Matt Prior (68) and Graeme Swann (27) they might have been in a tight spot in this warm-up at the Queenstown Event Centre ground.
The England seamers suffered too with an hour and a half of unexpected punishment from Corey Anderson and BJ Watling.
Graham Onions was taken apart in a spell of 4-0-36-0 with the second new ball as Anderson (67) and Watling (66no) raced past a century stand in only 18 overs.
Compton (1) and Pietersen (8) were both caught behind, off Mark Gillespie and Neil Wagner, as England struggled with the bat.