Sanchez scrappily manufactured a 34th-minute opener following a sustained spell of pressure, but diverted the ball over the line with his hand.
The close proximity of the Chile forward to a ricochet off Hull goalkeeper Eldin Jakupovic probably cleared him of any intent, but the sight of his raised right arm breaking the deadlock left Marco Silva's side understandably aggrieved.
Silva piled ignominy upon opposite number Arsene Wenger when his Olympiacos side won in north London last season and, amid the latest flurry of questions surrounding the veteran Frenchman's Arsenal future arriving on the back of last weekend's humbling loss to Chelsea, the hosts were rarely close to their fluent best.
Hull striker Oumar Niasse – one of five loanees in the visitors' starting line-up – drew fine saves from Petr Cech in either half before the Gunners wrapped up the points in stoppage time.
Sam Clucas blocked a header from Lucas Perez on the line, with a whistle from Mark Clattenburg forthcoming on this occasion. After an inevitable red card was brandished, Sanchez slammed home to calm the home faithful.
Hull twice ceded possession to Sanchez inside their own area and escaped early punishment before another errant pass, this time from Tom Huddlestone, resulted in Mesut Ozil having a shot blocked.
It was Arsenal's turn to serve up generous defending in the ninth minute as Lazar Markovic easily dispossessed Alex Iwobi and cut a ball across the face of goal - agonisingly beyond Niasse, who then forced Cech to push a header out of the top corner from Kamil Grosicki's delightful cross with the outside of his boot.
Hector Bellerin and Sanchez shot wastefully wide within a minute of one another as Wenger's men pulled Hull out of their defensive shape and Ozil showed clear frustration when he volleyed rashly off target from Sanchez's 25th-minute cross.
Theo Walcott's pursuit of his 100th Arsenal goal went on thanks to a brave block from Andrea Ranocchia, but the away side fell behind in controversial circumstances.
Huddlestone's poor clearance gave Kieran Gibbs a shooting opportunity and, after Andrew Robertson blocked the recalled full-back's shot on the line, Sanchez bundled the ball past Jakupovic, although replays showed his hand made the decisive touch.
Six minutes into the second period, Markovic made light of Laurent Koscielny's defensive efforts and surged forward – Niasse chesting down his ball into the box to draw a second fine stop from Cech.
Gibbs escaped with a yellow card for bundling Markovic over when the on-loan Liverpool man sprung away from the Arsenal backline, but Hull wasted the set-piece opportunity.
As the hour approached, Iwobi and Ozil showed deft touches before the former shot over from the left-hand side of the area.
Hull continued to probe with purpose, Niasse heading into the side-netting with 10 minutes to play, and their position third from bottom is not without hope after another impressive showing under Silva.
However, the otherwise impressive Jakupovic tore recklessly from his goal late on to set in motion the chain of events that would give Arsenal and Sanchez a more handsome haul.