The Ivory Coast international replaced Alexandre Lacazette in the 75th minute when the Gunners were trailing 2-1 and netted with two sublime free-kicks as Unai Emery’s side made it three wins out of three in Group F.
It was tough luck on the Portuguese side as they were the better outfit for long spells and deservedly took the lead in the eighth minute when Marcus Edwards, who ironically came through the youth team ranks at Tottenham, fired a right-footed effort past Emiliano Martinez in the Gunners goal.
Lacazette, making his first start for almost eight weeks, dragged his shot wide as Arsenal tried to hit back while Gabriel Martinelli was only just unable to latch on to Hector Bellerin’s cross.
Arsenal’s pressure did pay dividends in the 32nd minute though when Martinelli headed Kieran Tierney’s cross past Vitoria goalkeeper Miguel Silva.
However, just four minutes later the visitors restored their lead when Bruno Duarte lashed the rebound home after Davidson’s tremendous shot had hit the post.
Davidson went close to making it 3-1 before half time with another fierce strike that flew just wide while, after the break, Martinez had to make a smart stop to keep out Denis Poha’s shot.
Arsenal, once again without Mesut Ozil, struggled to create many openings and they were lucky not to concede another goal in the 63rd minute when Andre Almeida’s shot hit Rob Holding and went out for a corner.
However, Pepe made it 2-2 in the 80th minute with a superb 25-yard free-kick and, after Martinelli had gone close to grabbing a winner for Arsenal, the Ivorian repeated the trick in stoppage time to hand Emery’s team a slightly fortunate three points.