The Hammers controlled the game from the off but were only truly threatening from set-pieces. Rice headed onto the post from Aaron Cresswell’s free-kick before Craig Dawson’s header from a corner met the same fate.
Nothing had been quite coming off from open play until suddenly the hosts sparked into life. Michail Antonio drifted into space on the left of the Rapid Vienna penalty area and was found by a wonderful clipped ball from Andriy Yarmolenko. Antonio chested the ball down and showed the composure to square for Rice who tapped in for his second goal in as many games in Europe.
Rapid Vienna were awarded a second-half penalty after German referee Tobias Stieler adjudged that Ben Johnson had tripped substitute Marco Grull, though VAR showed the Vienna man had tripped over his own foot and the decision was overturned.
Jarrod Bowen was sent on to kill the game and should have done so after he rounded the goalkeeper, only to fire over the bar with his weaker foot.
West Ham finally started to turn the screw late on and Benrahma made sure of the result with a cool finish in the final minute of added time.
Here is how Jack Rosser rated the Hammers…
Hardly troubled but dealt with whatever came his way well. Another strong showing after his fine debut at Old Trafford.
Solid at the back and rightfully not punished following Grull’s tumble. Needs to offer more going forward if he’s to get more appearances on the right.
Wonderfully no-nonsense at the back and will feel he should have had a goal from a set-piece. Hit the post with one header and sent another over the bar.
Caught out on a couple of occasions but proving to be a good option for Moyes in a position where there is plenty of competition.
Untroubled defensively all evening and delivered some wicked set-pieces. Unlucky not to have an assist from one of them.
Did a lot of work for Mark Noble in the first half but largely dominated midfield and was in the right place at the right time for his goal.
Looked very off the pace in the opening half an hour but recovered to keep things ticking over. Struggled to make any real impact.
Good play in the build-up to Rice’s goal to find Antonio but offered very little else from the right-hand side.
Not really happening for him in a West Ham shirt so far. Gets into nice positions but doesn’t do enough once there. Needs time.
It wasn’t clicking for the Algerian for most of the night but he kept plugging away and sealed the result with a cool finish late on.
Constantly running the channels to try and cause problems and showed good awareness to tee up Rice for his goal.
Injected some pace into the attack and caused Vienna problems but should have done far better with his effort over the bar after getting around the goalkeeper.
Didn’t get West Ham going on the front foot as Moyes would have hoped.
Brought some stability to midfield after replacing Noble, who had struggled to keep up at times.