After a largely forgettable opening half, the Gunners gradually improved after the interval and took control of Group E with a 1-0 victory at the Estadio Jose Alvalade.
Welbeck had already seen a header chalked off for a foul but he was on hand to steer home in the 77th minute to settle the contest in favour of Unai Emery’s side.
Granit Xhaka started in the unfamiliar role of left-back as Emery made six changes for the game in Portugal, with Welbeck one of those drafted in
The win means a draw in the return fixture at the Emirates Stadium in a fortnight could be enough to seal Arsenal’s progression into the last-32 with two games remaining.
The draw leaves both sides on seven points in Group E, with the return fixture at the Emirates Stadium in a fortnight now seemingly pivotal as to who will become favourites to progress in first place.
Arsenal have impressed in their run of wins but one criticism has been their slow start to matches – especially in Monday’s Premier League win over Leicester.
That was the case again here but Sporting did not follow the example set by the Foxes and get about their visitors as the first 15 minutes played out with little action of note.
Stephan Lichtsteiner took a kick to the head as Bruno Fernandes attempted an acrobatic volley inside the Arsenal box but the experienced full-back showed now ill effects.
Arsenal tested Renan Ribiero in the Sporting goal for the first time at the midway point of the half after Mohamed Elneny had won a free-kick on the edge of the box.
Henrikh Mkhitaryan sent the set-piece towards goal but Ribiero punched clear in a rare moment of excitement with Sporting winning, and wasting, a number of corners at the other end.
Nani, who enjoyed some fine afternoons against Arsenal when playing for Manchester United, then fizzed a long-range shot just wide of Bernd Leno’s goal.
The recalled Pierre-Emerick Aubameyang sent a weak shot into the arms of Ribiero as referee Damir Skomina brought an end to a forgettable opening 45 minutes.
Fredy Montero headed wide from Nani’s free-kick at the start of the second half as Sporting looked to inject some life into the contest.
Aubameyang broke through the Sporting backline twice in a matter of minutes but could not beat Ribeiro on either occasion with both efforts straight at the Brazilian goalkeeper.
Following their recent pattern, Arsenal were much livelier and Andre Pinto did well to block Welbeck’s shot behind after smart work from Matteo Guendouzi opened up a chance for the forward.
Welbeck thought he had put Arsenal ahead as he rose to head in but his effort was ruled out as he pushed Sporting substitute Bruno Gaspar at the start of his jump.
The England forward made it count with his next chance as he benefited from a defensive slip from Sebastian Coates to nick in and finish coolly with 12 minutes left.
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