David Moyes' men are fourth in the Premier League but have arguably been even more impressive in Europe, with this their fourth victory in five matches.
Goals from Andriy Yarmolenko and Mark Noble shortly before half-time teed up a straightforward triumph, albeit one that was played out without a crowd as a lockdown kept home fans away after West Ham's travelling supporters had already been banned.
The Rapid faithful would not have been particularly impressed by what they saw if they had been present, as the margin of West Ham's victory could have been wider.
Jarrod Bowen passed up a huge chance for an early opener when he toed Arthur Masuaku's superb sixth-minute cross agonisingly wide, but West Ham had the lead they merited six minutes from the end of the first half.
Yarmolenko nodded Nikola Vlasic's teasing centre back across Paul Gartler for his first Hammers goal since January, before the scorer earned a clip from Maximilian Hofmann for a stoppage-time spot-kick, which Noble dispatched.
West Ham kept pushing and Bowen was wasteful again when he shot straight at Gartler at the end of a wonderful run and then when he blasted against the legs of retreating defender Filip Stojkovic after the goalkeeper had parried Tomas Soucek's header following a smart initial save.
Rapid threatened only fleetingly at the other end, as West Ham's comfortable position meant they could disregard events elsewhere in the group and hand a debut to Sonny Perkins, who almost scored with his first touch on a productive night for the visitors.