The Hammers arrived with qualification for the knockout stages already in the bag but in the knowledge that a win would seal top spot with a game to spare.
Moyes made eight changes but started with plenty of experience from Alphonse Areola, Tomas Soucek and Mark Noble.
Andriy Yarmolenko has the most European experience of all in the starting XI but it wasn’t showing early on. The Ukraine international was slow and sloppy and earned a rolliking from Noble after around 10 minutes. It may have taken a while, but the talking to had the desired effect.
Yarmolenko rose highest at the far post to nod in a lofted Nikola Vlasic cross before winning a penalty in injury time at the end of the first half, from which captain Noble converted.
The visitors should have extended their lead in the second half but this was about as comfortable a night as you could ask for.
Here is how Jack Rosser rated the Hammers in Vienna…
One save to make all evening and did just that. All you need from a keeper.
Plenty of energy down the right hand side but nothing too much to worry Ben Johnson over his first team spot.
Hardly troubled throughout, though a few rouge passes when on the ball at the back.
As routine an evening as you can get for the man hoping to replace Angelo Ogbonna in the side.
Caused plenty of problems down the left hand side throughout. Should have had an assist when Bowen turned his shot wide.
Controlling and composed performance from the captain. Vocal throughout and a fantastic penalty for his first proper Europa League goal.
Urged to take control of the game by Moyes but didn’t do too much on the ball. Should have scored when played in by Yarmolenko but shot straight at the keeper.
An enigma of a player. Shocking for the first 30 minutes and then scores before winning the penalty.
Showed some smart touches around the box as always but would have liked to register a goal or assist for his efforts.
A first goal contribution since he joined the club with a nice lofted cross for the opener. Should offer encouragement.
Worked hard in leading the line and showed quick feet but wasted an early chance to open the scoring.
Brought some energy to the front line but should have looked up to play in Vlasic on the break.
Kept control in midfield alongside Noble and showed plenty of willing but nothing too much to catch the eye.
Kept things ticking over well and some much needed minutes after looking very tired at Wolves.
Almost scored with one of his first touches, drawing a fine save. A good moment for the 17-year-old.