Yeovil began the game strongly and took the lead with just three minutes played, Pablo Bastiani sliding in from close range to finish from a corner.
The Hammers started creating chances, with trialist Petr Mikolanda and Zamora going close. The pair combined seven minutes before the break, with Mikolanda levelling for the visitors.
The hosts were ahead again, though, five minutes later after Kevin Gall got behind the Hammers defence and rounded Stephen Bywater before rolling it in.
Mikolanda, Zamora and Christian Dailly had chances in the second period and Zamora also missed a penalty.
Zamora, who was the Hammers' play-off hero in their promotion campaign, made amends five minutes from time when he finished at the second attempt.Reuse content