Pirates beat their Tunisian hosts thanks to a sublime finish by Thabo Rakhale just after the interval at the Stade Taïeb Mhiri.
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Bucs, however, required some fine goalkeeping from Brighton Mhlongo to claim the points, while the likes of Lehlohonolo Majoro and Kermit Erasmus had their share of opportunities to score in Sfax.
Tinkler said: "We had two great chances after the goal to bury the game. That could have made the result comfortable for us, and not so nerve-wracking for me on the bench.
"We knew we would create chances, we had two or three we should have buried.
"Hopefully in future we will stick them in the back of the net."
The result leaves the Sea Robbers second in Group B with six points from three matches - three points behind Egyptian giants Zamalek, who defeated AC Leopards 2-0 in Cairo earlier in the day. Leopards and Sfaxien have a point apiece.
Tinkler's men next face their Soweto rivals Kaizer Chiefs in the annual Carling Black Label Cup at FNB Stadium on August 1.
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The latest edition of KICK OFF Magazine (Issue 460) is out and we analyse the challenge ahead for Tinkler in a busy August for Pirates. Here's what else you can expect...