The Gunners headed into their clash against the Tigers under intense pressure following their back to back defeats at the hands of Watford and Chelsea.
Sanchez gave Arsenal the lead in the 34th minute when he bundled the ball over the line with his hand in controversial circumstances.
Arsenal failed to really click into top gear at The Emirates but made the points secure late on when Sanchez converted his penalty deep into second-half stoppage time.
The win lifted Arsenal up to third place in the Premier League table and nine points behind Chelsea ahead of the Blues’ trip to Burnley on Sunday.
And Smith singled out Sanchez for special praise after a typically industrious performance from the Chilean.
Speaking during Sky Sports‘ coverage of the game, Smith said: “As always, he’s tried to drag this team forward with his work-rate and desire.
“He gives such a high level of performance every week.”
Arsenal play Bayern Munich in Germany on Wednesday night.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news