The Gunners failed to find a way through on goal for the first time since the opening day of the season, but Qarabag's win at Vorskla Poltava in Group E's other fixture ensured that Unai Emery's side still went through.
Sporting defended doggedly all night, even when reduced to 10 men for the final few minutes when Jeremy Mathieu was shown a red card, and are now strong favourites to join their opponents in the knockout stage with this valuable point.
The night did come with negatives for an Arsenal side now unbeaten in 15 matches, however, as they lost Danny Welbeck to a nasty-looking injury half an hour into the match, while Stephan Lichtsteiner also hobbled off in the second half.
The slow tempo feel to the first half was not helped by the injury to Welbeck, who stayed down after heading Stephan Lichtsteiner's cross right at Ruben Ribeiro in the Sporting goal.
Following around four minutes of treatment, the English striker was taken straight down the tunnel and now appears certain to miss his national side's upcoming matches.
Arsenal's only other opening in the first half came via another right-sided delivery, this time through Matteo Guendouzi on the overlap as his cross was turned goalwards by Mathieu.
The fit-again defender was spared the embarrassment of an own goal by teammate Sebastian Coates, who got back to clear the loose ball off the line.
Emile Smith Rowe and Lichtsteiner, two of nine new faces included in the Gunners' starting XI on the back of the 1-1 draw against Liverpool last weekend, also fired shots well wide of the target in a low-quality first half.
Sporting appeared content to take a point back to Lisbon, but they had kept just two clean sheets in their last nine matches ahead of this one and were without a shutout in 30 European away outings.
Arsenal were less happy with a draw, coming close to a breakthrough early in the second period when Pierre-Emerick Aubameyang - on for the injured Welbeck - guided Henrikh Mkhitaryan's cross against the frame of the goal.
Aubameyang then sliced a shot into the side-netting, leaving the hosts with just that one Welbeck effort on target heading into the final 20 minutes of the match, at which point Arsenal lost Lichtsteiner to a hamstring injury.
Half-chances came and went for Aubameyang and Mkhitaryan in the final stages, with the latter failing to make any real contact on the ball once picked out by Alex Iwobi in front of goal.
Mathieu's dismissal for tripping Aubameyang on the edge of the box came too late in the match to make any real difference, as Arsenal were held for the third time in four matches on a mixed night for emery.
ARSENAL (4-2-3-1): Cech; Lichtsteiner (Maitland-Niles 74'), Sokratis, Holding, Jenkinson (Kolasinac 60'); Guendouzi, Ramsey; Mkhitaryan, Smith Rowe, Iwobi; Welbeck (Aubameyang 30')
SPORTING LISBON (4-4-2): Ribeiro; Gaspar, Coates, Mathieu, Acuna; Nani, Miguel Luis (Petrovic 85'), Gudelj, Bruno Fernandes; Montero (Bas Dost 69'), Diaby (Cabral 83')