Harmison flashed another catch behind, Mitch Claydon was lbw to Sajid Mahmood, who then took a simple catch at mid-off to put the seal on a miserable effort from Durham 20 minutes before lunch on day three.
It all depended on Rehman, but he did not get hold of an attempted pull shot and Guptill took a safe catch in the deep to put the spirited Kiwis back in the hunt for a place in the last four ahead of their next game against England on Monday.