Skippered by Peter Burling, the Kiwis won both races in Bermuda on Saturday.
USA began the best-of-13 series with a one-point advantage after winning the earlier qualifying regatta, which was erased by New Zealand's race one win. Races three and four are on Sunday.
The final is a repeat of the last time the trophy was contested in 2013, when Team USA came from 8-1 down to win 9-8.
Four years ago, New Zealand were eventually overhauled by an Oracle team that featured Britain's Ben Ainslie as tactician in what is regarded as one of sport's great comebacks.
Ainslie's British team were knocked out at the semi-final stage this year, losing 5-2 to the Kiwis.
The America's Cup, the oldest competition in international sport, was first raced in 1851 around the Isle of Wight and has only been won by four nations.
Emirates Team New Zealand moved into a 1-0 lead over Oracle Team USA after the first two races of the America's Cup.