The bowler finished the first innings with six wickets for 51 runs, as the hosts were bowled out for 254.
Broad told Sky Sports News: "I'm delighted to have picked up 'five-for' in a Test match, but more importantly to have bowled New Zealand out to be able to enforce the follow-on, and I hope we'll get some early wickets tomorrow.
"We had a discussion this morning that we were going to try to go at under three an over. If we managed to do that, we'd build enough pressure to get some wickets.
"It will be a 'reset' tomorrow, build patience because it's still a very good batting wicket. There's not a lot there, especially for the seamers."
The match resumes this evening, with the Black Caps 77-1 in their second innings.