The South Korean scored twice after the break to strengthen Leverkusen's lead at the top of the group and ensure his side will lead the way going into the final two games.
Jose Rondon pulled one back for the hosts, who dominated the first half in particular, but it proved insufficient as Leverkusen made it three consecutive European wins.
Having taken his tally in this season's competition to five, Son was full of praise for his side's showing.
"In the first half we were a little bit hectic, it wasn't our match at all," he explained.
"But in the second half we showed a good performance, you always could see that we wanted to win this match and we finally did.
"These three points are very important."
The club's sporting director Rudi Voller was in agreement and felt Leverkusen coped well with Zenit's early threat.
"We started very concentrated but after a few minutes Zenit became much stronger, especially Hulk who demonstrated why he is always so dangerous," Voller explained.
"After the break we did a good job and our win was absolutely well earned."
