The Chile striker has struggled this season after scoring 25 goals in his first year after leaving Barcelona.
After a draining Copa America he has lacked his usual energy, failing to score for his club until Saturday, but he was back to his best as Arsenal rallied to inflict a first league defeat this season on Leicester.
Sanchez put the Gunners ahead from close range after Theo Walcott had equalised Jamie Vardy's early goal.
The Chilean then headed the visitors 3-1 up early in the second half and put the visitors out of reach with a long-range blast.
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Vardy pulled one back before Olivier Giroud added a fifth goal for Arsenal.
It was all a reassuring sight for manager Arsene Wenger who relied so much on Sanchez last year.
"He is back to his level. He won a big competition with Chile, the Copa America," Wenger told reporters.
"I think to adjust to the game on a mental level takes some time. I could see in training a different player in the last week or two and he has shown that today.
"I believe going forward he always looked dangerous. Overall he is a striker who is mobile and works hard for the team. When the team plays well he can score goals."
Despite the convincing final score, Wenger said he had been worried as Leicester flew out of the blocks and dominated the early stages.
"I must say Leicester played well and to play a good football game there needs to be two teams," Wenger said.
"They had the stronger start, they pushed us on our back foot from the start when they scored the first goal and I must say I was concerned after that as I thought they were close to scoring a second one and it would have made it difficult.
"We found the resources to equalise and after that our technical quality and the pace of our strikers gave them problems and we managed to make it 2-1 before halftime.
"In the second half we controlled the game and looked always like we could add another one," said Wenger.
(Reporting by Martyn Herman,; editing by Tony Jimenez)
