The Gunners have taken 10 points their first four Group F games, while Vitoria picked up their first point after losing their first three encounters.
Arsenal were fortunate not to fall behind in the ninth minute when Vitoria’s Portuguese midfielder Pepe crashed a shot from outside the area against the underside of the crossbar.
Three minutes later Vitoria, who are fifth in the Portuguese Primeira Liga table, went close to breaking the deadlock again when Marcus Edwards’ drive was palmed away by Gunners goalkeeper Emiliano Martinez.
Arsenal, who needed two late Nicolas Pepe free-kicks a fortnight ago to come from behind to defeat Vitoria 3-2 on home soil, showed eight changes to the side that drew 1-1 with Wolves on Saturday.
They were captained by Rob Holding, who headed 18-year-old Bukayo Saka’s cross over the bar midway through the first half as Unai Emery’s side slowly began to get a foothold in the match.
Vitoria were the better team in the first period, though, and Davidson curled a fine shot narrowly wide before an unmarked Frederico Venancio, who had a spell on loan at Sheffield Wednesday earlier in his career, guided a header over the bar.
Arsenal suffered a blow in the second period when Dani Ceballos had to be substituted after appearing to pick up a hamstring injury, but they went close to taking the lead when Shkodran Mustafi’s header from a corner went over the bar.
Joe Willock lashed an effort high and wide before an unmarked Mustafi headed Pepe’s free-kick home with 10 minutes left to give the visitors the lead with their first on-target effort of the match.
However, Vitoria equalised in stoppage time when Bruno Duarte managed to turn Edwards’ cross home. The Portuguese outfit almost went on to win the match only for Rochinha to fire his last-gasp effort narrowly wide.