The Gunners came into the game on the back of two consecutive defeats.
And the home side started the slowly and the Tigers took advantage, with Niasse forcing Petr Cech into a fine save from a header.
Hector Bellerin and Sanchez both had good chances but shot wide.
Before Sanchez finally got his name on the scoresheet when his initial shot was saved but the ball popped up and hit his hand before going into the back of the net in the 34th minute.
Alexis Sanchez celebrates scoring Arsenal's first goal
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Sat, February 11, 2017
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Petr Cech – 7.5
After the break Arsenal continued to lack incision and creativity, giving the away side hope of a shock result.
And Arsenal could have gone down to 10 men when Kieran Gibbs brought down Lazar Markovic as the last man but fortunately for him, Mark Clattenburg pulled out a yellow card.
Hull tested Arsenal with several crosses into the box but left themselves open defensively and in stoppage time, substitute Lucas Perez saw his goal bound header blocked on the line by Sam Clucas.
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After some deliberation Clattenburg pointed to the spot for deliberate handball, sent off Clucas and Sanchez side footed the ball past Jakupovic.