Hopkins, a 2.03m power forward/center, entered the contest averaging 18.7 points per game and he had 16 by half-time on Tuesday.
In the first meeting between the sides on December 1, Apoel rolled to a 104-71 victory and inside the final minute of the first half of the rematch, another mauling appeared to be on the cards because the visiting side had a 44-23 stranglehold on proceedings.
A pair of LaVell Blanchard three-pointers for Khimik cut their deficit to 46-33 early in third quarter.
After Apoel opened up a 20-point lead again, Khimik worked their way back and another Blanchard three-ball cut the visitors' advantage to 62-51 with 1:47 remaining in the third quarter.
Apoel stayed on top but Khimik scrapped away and when Dmytro Khodov made a lay-up with 3:30 remaining to reduce the arrears to 76-69, an improbable comeback began to look like a real possibility.
Hopkins steadied Apoel's nerves, though, by making two free-throws and Gerben Van Dorpe hit a shot from the arc to extend the advantage back to 81-69.
Blanchard's tip-in and Khodov's trey in the final minute closed the gap to 84-78 but that's how it ended as Apoel clinched their place in the next round.
Khimik dropped to 1-4.
Blanchard and Darrel Mitchell both played for Proteas EKA AEL last season and competed in the EuroChallenge Final Four.
The former had 24 points on Tuesday while the latter contributed 20.
Dmitriy Baselevskiy, BC Khimik coach:
"Our game in the first half was quite different from our game in the second half when we played what we can play. I want also to say that it's easier to play defense against our team, it's enough playing hard against Darrel Mitchell. The unpredictability of our young players really hurt us. We have two leaders but all other players must understand that they have to also work hard on the court. I also want to say that our game under the basket wasn't good today. Certainly Apoel is a much stronger and more experienced team."
Dmytro Khodov, BC Khimik:
"I would like to say that Apoel is very good and strong team. We played very bad in the first half. In the second half we started playing good defense and it helped us to win that part of the game but it didn't help us to win the game in general."
Gerben Van Dorpe, Apoel:
"The last couple weeks we won all our games, in Europe and in Cyprus. We came here to win the game. The first half we played hard and we put a gap between us and our opponents. In the second half we didn't play so well but it was enough to win this game."
Kristos Stilyandes, Apoel coach:
"I want to congratulate both teams for a wonderful game. The key in winning this game is playing stronger and harder from the start. At half time I told my team that the game was not over because I know that Khimik is unpredictable. And they really showed a wonderful fight in the second half. We won the game and that's great. It's very important for us to finish first in our group."