Attacker Michail Antonio made the most of a defensive mistake to put West Ham in front midway through the first half. The no.9 will, however, be unavailable for selection on Sunday due to his red card against Southampton last weekend.
Shortly after the restart, West Ham doubled their advantage in the Croatian capital.
Declan Rice’s elegant solo run and finish settled the tie in the 50th minute to give the Hammers the early upper hand in a group which also features Genk and Rapid Vienna.
Kurt Zouma made his Hammers debut after his transfer from Chelsea earlier this month, with fellow summer signing Nikola Vlasic appearing from the start for the first time in a claret-and-blue shirt.