Mathew Sinclair, who made 47, pushed Monty Panesar to Strauss at first slip three overs later before Harmison completed his five-wicket haul with both Griggs and Jeetan Patel edging behind attempting expansive drives outside off-stump.
"It's got marginally better the more and more I've bowled," said Harmison, who arrived in New Zealand later than the other Test specialists because of the birth of his fourth child.
"At this moment in time I'm still trying to find my feet and find the right length on these wickets because I've only been in the country eight days.