Fly-half JJ Hanrahan's second-half penalty edged Connacht to an outstanding 13-12 United Rugby Championship victory over the Sharks in Durban.
The Sharks will be looking to end their four-week United Rugby Championship European tour on a positive note when they take on Zebre Parma on Friday night.
The Sharks, Lions and Stormers will be looking to reverse their fortunes in the United Rugby Championship this week.
The Sharks continued to struggle on their overseas tour as they fell to a 19-5 defeat United Rugby Championship defeat against Ospreys at the Stoop.
After a tight first half, the Sharks were thoroughly outplayed in the second as Leinster claimed a 34-13 United Rugby Championship win at a wet RDS Arena.
Three of the four South African teams are on overseas duty for the second week of the United Rugby Championship, with some tough fixtures awaiting them.