Gloucestershire looked in trouble at 157-5 before the pair came together.
But Marshall made 123 and fellow New Zealander Noema-Barnett struck 84 as the hosts finished on 336-5.
England's Moeen Ali (0-32), playing his first game for Worcestershire in 2016, failed to pick up a wicket.
Hamish Marshall and Kieran Noema-Barnett shared an unbroken sixth-wicket stand of 179 to put Gloucestershire in a strong position on the first day against Worcestershire at Bristol.