A confident first-half performance saw the hosts hit a post through Lars Bender before taking the lead after 34 minutes when the Korean's shot was spilled into the path of Stefan Kiessling, who finished from close range.
An accomplished performance from Son was rewarded just before half-time when he was picked out by Karim Bellarabi to lash home.
The result leaves Leverkusen one point behind Zenit and Monaco in Group G, while Benfica's chances of progressing to the last 16 now hang in the balance, without a point from two games.
After a blistering start to their campaign, a recent goal drought had seen Leverkusen find the net just twice in their last four games coming into this contest, but boss Roger Schmidt will have been pleased by the way his team performed at the BayArena.
The veteran keeper was beaten just before the 15-minute mark, but Bender's effort came back of the post.
However, the hosts did break the deadlock with 25 minutes on the clock when a sweeping attacking move saw Julio Cesar parry Son's initial shot straight to Kiessling, who gladly tucked away the rebound with a simple finish.
However, Leverkusen restored their two-goal cushion just 60 seconds later, when Jardel brought Kiessling down in the box, allowing Calhanoglu to make up for his earlier miss by stroking home the resulting penalty and cap off Leverkusen's first win over the Portuguese outfit.
