A Punt shot from a penalty corner, deflected off an English stick, regained the lead midway through the second quarter.
Michelsen was quickest to react after her shot bounced back off the England crossbar seven minutes from the end and her tap in put the Black Sticks out of reach of an outplayed England.
New Zealand will rue their inability to make more use of eight penalty corner opportunities, but they were full of running, attacked more purposefully and could have had another couple of goals.
The semfinal is on Sunday morning, and a win over world No 2 Australia will put the Black Sticks in their first Champions Trophy final.
World champions the Netherlands will play either hosts Argentina or China in the other semifinal after beating Germany 1-0 today.
Australia progressed to face New Zealand after a 4-1 win over Japan.