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.
“We were disappointed to lose our record of 17 unbeaten two weeks ago against Olympiacos, so it’s good to get back on track,” said Moyes.
“We’re top of the group, we still have two matches to play but at the moment I think this is the hardest group we’ve had, in our third year in it, and it’s proved to be the case. We’ve done the job tonight. It’s a great result for us.
“Europe has been great for this football club, we’ve had some great nights and long may they continue.”
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.
“I don’t think VAR needed to come to the rescue, it was onside, it was a goal,” added Moyes.
“We needed it because the game was very tight, there was very little in it.
“He took the goal brilliantly tonight but there were lots of things I wanted him to do better. We’ve got room for improvement.”
It was a fourth assist in four European outings for Ward-Prowse, who was overlooked by England again earlier in the day, more than a year after his last call-up.
Paqueta pointedly went to the 3,000 travelling fans to celebrate, probably because the West Ham players were targeted by laser pens from Greek supporters in Athens.
West Ham survived a late scare when Mady Camara rattled a post but they held on to complete their European revenge mission.