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.