The Catalans are tied with Atletico Madrid on 49 points with the two set to meet for the first time in the league this season next weekend at the Vicente Calderon.
Lionel Messi was once again watching from the sidelines yesterday as he nears a comeback from a hamstring injury and Neymar was left on the bench having recently returned from a Christmas break in Brazil.
However, Sanchez and Pedro Rodriguez once again proved able deputies as they slotted home inside the opening 15 minutes.
And the Chilean sealed his first hat-trick for the club with a stunning free-kick 21 minutes from time.
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Barca now lead Real Madrid by eight points, but Madrid can cut the gap on the leaders to five with victory over Celta Vigo on Monday.
"We played very well. We had variation, precision, control and we had a lot of chances," said Barca boss Gerardo Martino.
"We were always concentrated through the game and limited the opponent to very few sights of goal.
And the Argentine was particularly pleased with the contribution of Pedro and Sanchez in the absence of Messi and Neymar.
"I was happy for Alexis because, as a coach, you always like to see players like he and Pedro who work so hard for the team get their reward.