Lucas Paqueta scored the only goal of the game as West Ham avenged their loss to Olympiacos in the Europa League.
The Brazil midfielder crashed in a second-half volley to keep the Hammers on top of Group A and to the brink of qualifying for the knockout stages.
Moyes' side are also guaranteed European football after Christmas with the worst-case scenario a third-placed finish meaning a return to the Europa Conference League and a chance to defend the trophy they won last season.
They enjoyed a measure of revenge, too, having accused the Greek team of celebrating their 2-1 win in the reverse fixture two weeks ago as if they had won the Europa League itself.
Not only that, but West Ham have now won their last nine home games in Europe since the start of last season, one more than Manchester City.
Paqueta, the best player on the pitch, broke the deadlock in the 74th minute after Bowen's square pass found James Ward-Prowse.
The former Southampton midfielder chipped the ball forward into the area for Paqueta to fire home on the volley.
The goal was initially ruled out by an assistant referee's flag, but a VAR check showed the Brazilian was onside and referee Matej Jug, who had infuriated West Ham with some strange decisions all evening, got the biggest cheer of the night when he signalled a goal.
