Slaven Bilic's side were keen to build on their impressive point against Manchester United last week, but they came into game suffering a number of key injuries to key players such as Aaron Cresswell, Cheikhou Kouyate and Michail Antonio and were unable to cope with a rampant Arsenal team.
Sanchez was the star performer for the north London Club with an impressive display, while Mesut Ozil and Alex Oxlade-Chamberlain also got on the scoresheet to make it a miserable afternoon for the east London side.
Bilic will be doing everything he can to lift his players this week ahead of another tough game against Liverpool at Anfield next Sunday and will be hoping the return of some key players will help turn his side's fortunes around.
The Hammers manager was forced to make several changes to his team including reverting Edimilson Fernandes to a right wing back role and bringing Arthur Masuaku back into the starting eleven following a two month injury absence.
But just when Bilic thought his luck could not could get any worse on the injury front, he suffered the worst possible start to the game when James Collins picked up a hamstring injury and was forced to leave the field after just seven minutes.
The injury forced the Hammers manager to change the shape of the team and Arsenal certainly made the most of it.
The away side could have opened the scoring on 17 minutes when Mesut Ozil's corner picked out Shkodran Mustafi who rose the highest inside the box and directed a header just past the post.
But the Hammers hit back and also had a good chance to break the deadlock on 19 minutes when Dimitri Payet played a great through ball into the path of Manuel Lanzini who weaved his way into the penalty area and held off the challenge of two Arsenal defenders before seeing his shot well turned round the post by Petr Cech.
Arsenal made their dominance count when they opened the scoring 24 minutes following a mistake by Angelo Ogbonna after he struck the ball straight against Francis Coquelin.
The rebound fell to Sanchez who took the ball around Winston Reid and squared for Ozil who had the easy task of knocking the ball into an empty net.
Arsenal could have doubled their lead shortly after half-time when Ozil's free-kick picked out Theo Walcott who headed the ball just over the bar.
This was not proving to be an easy afternoon for the home side and Randolph kept them in the game with a superb double save on 69 minutes to keep out close-range shots from Aaron Ramsey and Ozil.
Arsenal continued to mount pressure on the West Ham goal and added a second on 72 minutes when Mustafi played the ball into Sanchez who took the ball past Arthur Masuaku and fired a powerful low shot past Randolph into the corner of the net.
Sanchez added his second of the game on 80 minutes when he found space ahead of Ogbonna and drilled a shot past Randolph.
The Hammers pulled back a consolation goal back on 83 minutes after Dimitri Payet's free-kick hit the bar and substitute Carroll reacted the quickest to head the ball over the line.
But it was not enough to stop Arsenal scoring two late goals.
Arsenal made it four on 84 minutes when Oxlade-Chamberlain found himself unmarked on the edge of the box and curled a shot past Randolph into the corner of the net.
Sanchez completed his hat-trick and made it five on 86 minutes when he delicately chipped the ball over the advancing Randolph to complete a disappointing perfomance for the home side.
West Ham: Randolph; Collins (Arbeloa 7), Reid, Ogbonna; Fernandes (Ayew 63), Noble (Carroll 72), Obiang, Masuaku; Lanzini, Payet, Fletcher
Subs not used: Adrian, Nordtveit, Feghouli, Zaza
Bookings: Fletcher, Reid, Arbeloa
Arsenal: Cech; Gabriel, Mustafi, Koscielny, Monreal; Coquelin, Xhaka; Walcott (Ramsey 660, Özil (Iwobi 87), Oxlade-Chamberlain; Sánchez
Subs not used: Gibbs, Pérez, Ospina, Holding, Elneny
Bookings: Coquelin, Koscielny, Mustafi
Referee: Craig Pawson