First-half strikes from the Chilean forward and Welsh midfielder helped the Gunners to extend their unbeaten run to 10 games and condemn Hull to a first defeat in three
The Chilean opened the scoring with a free-kick that flicked off the head of Michael Dawson, before Aaron Ramsey doubled the Gunners' lead with another deflected strike.
Sanchez made it three in first-half injury time, rounding Steve Harper and rolling the ball into an empty net for his 16th goal of the campaign.
Stephen Quinn clawed one back for the Tigers with a header in the 56th minute, but Arsene Wenger's side held out to secure all three points.
The win was Arsenal's ninth in ten games and moves them level on points with Manchester City in second place, while Hull drop to 17th, just a single place and point above the drop zone with three games remaining.
Hull will require greater luck in their remaining fixtures after Sone Aluko wasted a good opening early on and Arsenal were rewarded for their own positive start 28 minutes in when Sanchez's free-kick struck the head of Dawson, wrong-footing Harper on its way into the net.
Things went from bad to worse for the home side five minutes later, with another deflected strike putting them further behind.
Santi Cazorla spotted Ramsey's forward run and the Wales midfielder controlled the Spaniard's fine pass instantly before turning and letting fly with a shot from inside the penalty area which hit Robbie Brady before looping into the far corner of the net.
Hull were struggling to cope with Sanchez's movement and Harper did well to deny him when Cazorla split open the Tigers' defence with a sublime pass.
Bruce's side failed to learn their lesson as Sanchez struck again in first-half stoppage time, beating the goalkeeper with his first touch and finishing with his second after Ramsey turned provider with an incisive pass.
Hull pulled a goal back out of the blue 11 minutes into the second half, with Quinn the unlikely scorer, timing his run to perfection to head home Ahmed Elmohamady's cross from close range.
Arsenal felt referee Lee Mason should have awarded a free-kick for a David Meyler challenge on Laurent Koscielny in the build-up to the goal, and they almost conceded again as Paul McShane headed just over the crossbar.
Sanchez spurned two good openings for his hat-trick but his double was enough, though Nikica Jelavic's return from two months out may provide a crumb of comfort for Hull ahead of the weekend's visit of Burnley.