The Hammers suffered a 2-1 defeat to the Greek giants in the reverse match at the end of October, but the Premier League side were able to gain revenge in the English capital.
Paqueta netted the only goal of the contest in the 72nd minute, and the result has left David Moyes's side top of Group A on nine points, level with second-placed Freiburg and five clear of third-placed Olympiacos.
Next up for West Ham, who are guaranteed to finish at least third, is a trip to Backa Topola at the end of November, while Olympiacos will head to Germany to take on Freiburg.
Said Benrahma had an early sighter for West Ham, sending one wide of the post from distance, with the Hammers making a fast start to the contest in the English capital.
Olympiacos had a shout for a penalty in the sixth minute when the ball appeared to strike Paqueta's arm, but the referee was happy for the play to continue and VAR agreed with the initial decision.
Alexandros Paschalakis made an excellent save to keep out a curling Benrahma strike in the 13th minute, before the Olympiacos goalkeeper denied Nayef Aguerd from the resulting corner.
Jarrod Bowen was next to try his luck, heading over the crossbar in the 19th minute, with West Ham certainly the more inventive in the final third of the field.
Aguerd won another header from a corner in the 24th minute, but the centre-back's effort dropped wide of the post, with Olympiacos surviving a dangerous moment.
Paschalakis again went head-to-head with Benrahma in the 32nd minute, and it was another smart save from the goalkeeper, pushing the forward's powerful effort around the post.
Aguerd should have scored from the resulting corner, but he headed wide of the post once again, before Daniel Podence passed up a good chance down the other end, firing over the crossbar on the half-volley.
Olympiacos had the first half-chance of the second period in the 51st minute, but Kostas Fortounis's chipped effort from a dangerous position landed on the roof of the net.
Ward-Prowse had West Ham's first real opportunity of the second half just past the hour, but the Englishman's effort from the edge of the box never had enough power to trouble the Olympiacos goalkeeper.
The home side managed to make the breakthrough in the 73rd minute, with Ward-Prowse's excellent pass releasing Paqueta, who found the back of the net with a smart volley.
The goal was initially disallowed for offside, but a VAR check led to the decision being overturned, which sparked more celebrations inside the stadium.
Olympiacos came close to a leveller late on through Mady Camara, but the midfielder struck against the post from close range in a huge let-off for the Hammers, who were able to close out the final stages to secure a huge three points in Group A.