Finn and Anderson quickly reduced the hosts to 11-3 in the third and final ODI before they were bowled out for 185.
England made it to the winning total with plenty of overs to spare and Cook was full of praise for his opening bowlers.
"They have been magnificent. I thought Finny's pace... I think he's up around the 90mph mark pretty much all the time, and Jimmy's world class and he showed it again here," Cook told Sky Sports News.
"It's quite easy to captain in the first few overs when you've got that sort of control."
The two sides will next contest a three-Test series that begins in Dunedin on Sunday, March 10.