Deborah Fleming finished off a Heather Fisher break two minutes after the restart to narrow the lead, but the Kiwis hit back almost immediately with Blyde and Woodman crossing in quick time.
Last year's world women's player of the year, Woodman's third try extended the New Zealand lead to 33-5, with England gaining some respectability through Jess Breach's game-closing effort.
Earlier, Woodman had snared four tries in New Zealand's opening 48-7 win over Japan. The Black Ferns Sevens ran in eight tries against their outmatched opponents and led 22-7 at half-time.
Woodman used her electric pace to cross twice in each half, handed ample space against a Japanese side which struggled for possession.
Blyde bagged a double while New Zealand's other tries went to Ruby Tui and Stacey Waaka.
They won five of six tournaments last season and were runners-up in Sydney.
They will next play Ireland in the quarter-finals, tomorrow.