Rapid Vienna 0-2 West Ham: Andriy Yarmolenko and Mark Noble both hit the target in Austria
It was an important victory for the Hammers as they are now straight through to the knockout stage having avoided a play-off in February against a team dropping down from the Champions League.
Moyes was even able to make eight changes to his side, resting the likes of Declan Rice and Michail Antonio, and still comfortably get the job done.
With Vienna in a new coronavirus lockdown the match was played in an empty stadium, with Rapid unable to call on their boisterous fans to lift them, and West Ham simply had too much class.
They almost got off to the perfect start when Arthur Masuaku drove a low cross into the box for the sliding Jarrod Bowen to poke just wide after five minutes.
Nikola Vlasic and Yarmolenko both fired narrowly over in a bright opening from the visitors.
The only moment of mild alarm came when Kelvin Arase weaved into a shooting position, and his effort was saved by back-up keeper Alphonse Areola on his way to a fifth clean sheet in six appearances for the Hammers.
Their dominance finally told six minutes before half-time when Vlasic crossed from the left and Yarmolenko was left with a simple header back across goal.
It was a first Hammers goal since January for the Ukraine international, who has played only 52 minutes in the Premier League this season.
Yarmolenko had a big hand in the second goal in first-half stoppage time after he turned Rapid skipper Maximilian Hofmann in the area and was brought down.
Captain Noble, a man clearly relishing this European adventure in his 18th and final season at the club, made no mistake from the spot.
After the break Bowen’s quick feet in the area accounted for three defenders, but his shot was straight at Rapid goalkeeper Paul Gartler.
Gartler also denied Tomas Soucek before Bowen’s follow-up was blocked on the line.
Teenage striker Sonny Perkins came on as a substitute for his Hammers debut and almost marked it with a goal when he met Vladimir Coufal’s cross with a fine header, but Gartler made a stunning reflex save and West Ham had to settle for two.