Evian striker Khlifa, one of the fringe players facing being dropped when Tunisia decide on their final 23-man squad on Wednesday, scored with a diving header after a curling free kick by Zouhair Dhaouadi to give Tunisia an early lead.
Dhaouadi added a second goal on the hour with a quick burst of pace past the Sudan defence and a shot from the edge of the area.
A wild tackle on Dhaouadi 13 minutes later by Yousef Alaeldin left Sudan with 10 men and the advantage was exploited when substitute Amine Chermiti scored the third goal seven minutes from the end.
Sudan, who are also headed to the Nations Cup finals in Equatorial Guinea and Gabon later this month, play a warm-up match in Senegal later this week while Tunisia take on the Ivory Coast in Abu Dhabi on Friday.
The African Nations Cup kicks off on January 21.