.The 25-year-old international striker also scored the first goal for the Tunis outfit, whose victory gave them a three-point over the Pretoria club in Group C.
Sibusiso Vilakazi equalised for Sundowns during the first half, but the injury-weakened hosts lacked the sharpness that won the title for the first time last year.
Esperance have seven points, Sundowns four, Saint George of Ethiopia two and V Club of the Democratic Republic of Congo none.
Saint George host V Club Sunday in Addis Ababa and the bottom seeds will rise to second if they secure maximum points.
Sundowns looked jaded and devoid of ideas after the South African season ended last weekend with them second behind Wits in defence of the league title.
Although twice African champions Esperance have also just finished their local season, winning the title, they were fresh and threatening when counterattacking.
It took the visitors just six minutes to go ahead with Khenissi darting on to a clever flick and unleashing a sizzling shot past Ugandan goalkeeper Denis Onyango.
Sundowns levelled on 21 minutes when Percy Tau burst through the middle and passed across the goal for Vilakazi to tap in.
Off-form Colombian Leonardo Castro wasted a second-half change to put Sundowns in front by failing to control the ball inside the box and firing wide.
The South African outfit also squandered several set-piece opportunities before Ivorian Bangaly Soumahoro fouled Fakhreddine Ben Youssef and Khenissi converted the spot-kick.
Al Ahly Tripoli of Libya shocked CAPS United of Zimbabwe 4-2 in Harare to rise from the bottom of Group B to second place.
The visitors scored three goals in nine minutes during the first half through Tunisian Sameh Derbali, from a penalty, Salem Ablo and Mouad Allafri.
Derbali added a fourth nine minutes from time before late goals by Ronald Pfumbidzai, from another penalty, and Hardlife Zvirekwi flattered CAPS.
Beanpole Anis Saltou -- the Perer Crouch of Libyan football -- created the first three goals and wasted several chances to score himself.