The Black Star scored twice as the Belgian side picked up a 2-0 first-leg win that sets them in pole position to advance to the Round of 16.
The winger opened the scoring the fifth minute when he reacted first to finish past Yuri Lodygin after Zenit failed to clear their lines following a set piece.
He doubled the home side’s lead in front of the delirious fans in the Constant Vanden Stock Stadium just after the half-hour mark.
The match was Acheampong’s first match back with his club after returning from Nations Cup action with Ghana.
He initially headed to Gabon as one of the squad’s backup players, but an injury to Abdul Rahman Baba in the opener against Uganda saw the 24-year-old shoe-horned into the side at left-back for the rest of the tournament.
Acheampong equipped himself well, but will surely be delighted to return to a more offensive role with his club side where, as he demonstrated against the Russian heavyweights on Thursday, he can express himself in the final third.
The former King Faisal Babies starlet ended 2016 strongly with Anderlecht, finishing the year with two assists and a goal in his last two performances before heading on to international duty.