But the result, which lifted them to third in the table, was far from convincing and did little to settle the debate over Arsene Wenger's future after days of uncertainty about whether he will remain in charge next season.
The manager completed his four-match touchline ban by watching from the stands and was delighted to see Sahchez pop up on the line for the opener on 34 minutes. But the goal was controversial, with the ball going in inadvertently off the Chilean's hand after popping up from a goalline save by Hull keeper Eldin Jakupovic.
Afterwards Hull defender Andrew Robertson said referee Mark Clattenburg apologised for not disallowing the goal when he saw the halftime replay.
"The referee apologised to us after halftime and said it was a handball," said Robertson. "He obviously realises he was in the wrong. It must be tough for him, but often decisions don't go your way when you come to these big stadiums."
Oumar Niasse twice went close for an enterprising Hull side, who had Sam Clucas sent off for conceding the injury-time penalty from which Sanchez scored his 17th league goal -- and fourth against Hull -- this season.
Asked if Arsenal had been fortunate, Wenger said: "Maybe. Sorry for that but I cannot influence that. I felt we were resilient, focused.
"It was not easy against a good side. There was an edgy atmosphere but as a player you have to cope with that."
Wenger was non-committal about his future.
"I have big respect for this country and this club and I am grateful because I have worked here for 20 years," he said.
(Reporting by Neil Robinson, editing by Pritha Sarkar)
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