Bowling his eighth delivery of the match, Anderson found the edge of Guptill's bat and Ian Bell took the catch at second slip to leave New Zealand on 2-1 in the third over.
India's Harbhajan Singh is the only active bowler above Anderson in the list of all-time wicket-takers in tests. Sri Lanka great Muttiah Muralitharan is No. 1 with 800 wickets.
Anderson is playing in his 104th test.