The Group A matchday 2 fixture was moved from Tripoli because of ongoing militia-instigated violence in the oil-rich state.
Khazri converted a 50th-minute penalty for a foul on Taha Khenissi by Libya captain Ali Salama, who was yellow carded, then sent off as he had also been cautioned in the first half.
Three Tunisians were yellow-carded during the first World Cup meeting between the North African neighbours.
Libya were furious at having an early first-half goal ruled offside, with big-screen replays suggesting the Kenyan referee erred.
Victory lifted Tunisia to the top of the group with six points, Democratic Republic of Congo have three and Guinea and Libya none.
Guinea host DR Congo in Conakry Sunday in the last of 10 African qualifiers scheduled for this weekend.