Declan Rice’s first-half tap-in and Said Benrahma’s injury-time effort gave them victory at the London Stadium.
Following on from their success at Dinamo Zagreb a fortnight ago, Moyes’ men are in command of Group H ahead of back-to-back meetings with Belgian side Genk.
Rice also hit a post with a near-post flick and Craig Dawson saw his header bounce back off the woodwork.
Substitute Jarrod Bowen should have scored in the second half, but blazed wide with only defender Kevin Wimmer on the line to beat.
Pablo Fornals had a shot saved in stoppage time, moments before Benrahma found the bottom corner with virtually the last kick.
Moyes told BT Sport: “I want to try and be in Europe after Christmas by finishing one or two, so we want to win the group if we can.
“We are not going to let up, we are enjoying it and won’t be letting it go easy, but I have to manage Premier League games too.
“We are capable of handling it and the squad we have can handle it too. It will be tough, but I hope we can manage it.
“Pleased we won, but we did not play as well as we would have liked. We made a few changes but we are in a lot of competitions and we have to make it work for the whole squad.”
The game did not pass without incident.
West Ham’s 29th-minute opener triggered ugly scenes as a number of the 1,300 Rapid Vienna fans jumped over barriers and ran the short distance to goad the home contingent. It triggered numerous objects being thrown in the air by both sets of fans.
A significant police presence ensured the situation did not escalate and, although more objects were thrown when Rapid had a penalty overturned late on, it was not on the same scale.
Thankfully, Benrahma’s effort did not result in a repeat of what happened following the opening goal.
Moyes added: “We want to be a club in Europe and be there regularly. Because of that we want to behave correctly. We don’t know who started that, but we don’t want that reputation.
“We want to be invited to these competitions and we want to be a club who can travel in Europe.”