Sanchez opened the scoring for Arsenal in the 18th minute after deflecting in a shot by Alex Iwobi who received the ball off a Héctor Bellerín cross, powering the ball into the back of the net past the Tigers goalkeeper Eldin Jakupović who had up to that point looked unbeatable.
Hull had their own attempts on goal, with Abel Hernandez coming close on a counter attack but unable to guide the ball past Petr Cech, but spent the majority of the first half defending the Arsenal attack.
Jake Livermore made life difficult for the home-side after being given a red card for handball in the box after only 40 minutes of play, gifting Sanchez a chance to double the lead.
Jakupović, who has faced criticism for his form so far this season put in a hero performance, saving the attempt in addition to a number of other spectacular stops throughout the match.
Hull forward Adama Diomande was replaced by defender Harry Maguire in the hopes of stopping any more Gunners goals shortly before the half-time break.
Santi Cazorla came close to making it ten against ten just minutes into the second half after tripping up Robert Snodgrass, having been given a yellow in the first for taking down Ahmed Elmohamady but was given the benefit of the doubt by referee Roger East, much to the displeasure of the home fans.
Theo Walcott scored his 100th goal for the Gunners with a beautiful tip-in at the 55th minute, playing a beautiful one-two with Iwobi before darting into space and chipping it into the net past a helpless Maguire.
Despite looking out for the count, Hull kept attacking when the opportunity arose, with substitute striker Dieumerci Mbokani latching onto a pass from Ryan Mason into the box, being taken down by Cech with the referee awarding a penalty which was converted by Snodgrass, scoring his fourth goal in four Premier League matches this season in the 79th minute.
A comeback was not to be with Alexis Sanchez sealing the win only moments later, re-establishing the two-goal lead with less than eight minutes to play after a Walcott shot was deflected by Jakupović straight to the Chilean.
Granit Xhaka rubbed salt in the wounds to Mike Phelan's side with a stunning strike in injury time with a long-range strike from close to ten metres outside the box, with the 4-1 scoreline perhaps not reflective of Hull's efforts.