Chances were scarce for either side in the opening stages, but the visitors were dealt two major blows when top scorer Diego Costa limped off before winger Arda Turan soon joined him on the sidelines through injury.
The hosts had the better of the first-half chances with Adriano and Pedro both threatening, but it was Sanchez who fired them ahead from a seemingly impossible angle after Lionel Messi's knock-down.
However, Diego Simeone's men found themselves back in control in the second half when Diego Godin rose to emphatically head Gabi's corner beyond Joes Manuel Pinto as Atletico claimed their tenth title.
Gerardo Martino's side knew that anything other than a win would see them hand the title trophy back to Madrid, but this time to the team in red and white after a stunning campaign under Simeone.
Under 500 visiting fans were said to be in the away section of the Nou Camp, with the atmosphere capturing the sense of occasion perfectly as the teams were greeted onto the field with deafening cheers.
Barca grew into the game as the first half developed and could have been ahead when Pedro Rodriguez wastefully headed over Dani Alves' precise cross from the right.
When the Catalans did go in front just after the half hour it was in spectacular fashion as Lionel Messi cushioned the ball into Sanchez's path on the right side of the area, but despite the narrow angle he managed to thrash the ball high past Thibaut Courtois at the Belgian's near post.
Atletico forced a series of corners without carving out a clear-cut chance in their search for an equaliser before the break, but the half-time whistle also brought frustration on the part of the Barca players as both Messi and Sergio Busquets were booked for dissent.
David Villa came within inches of an equaliser a minute after the restart when his low effort came back off the post and the former Barca striker had another opening moments later that was smothered by Pinto in the Barca goal.
But, the visitors only had to wait a minute longer to be level as Godin rose highest in the box to power home Gabi's corner.
Barca then suffered an injury blow of their own as Busquets had to be replaced by Alex Song, whilst Neymar was also introduced by Gerardo Martino in the search for a winner.
Messi did have the ball in the net with 25 minutes remaining, but he was flagged offside as he latched onto a loose ball inside the area.
Alves stung the palms of Courtois with an effort from 25 yards as Barca camped themselves in the Atletico half for the final 10 minutes.
However, despite piling bodies forward, Barca failed to carve out another clear opening in the final stages as Atletico saw the game out to stretch their unbeaten run against Barca to six games this season.
Full-time saw a warm gesture from the home fans as all sides of the Nou Camp stood to applaud the victors who celebrated on the pitch.