Sanchez was on hand to turn in Lionel Messi's cross after just six minutes and despite a few scares from an attack-minded Benfica they sealed the three points 10 minutes into the second period when Messi again set up Fabregas to rifle in at Artur Moraes' near post.
However, the Catalans' night was soured towards the end when captain Carles Puyol carried off on a stretcher with what appeared to be a broken arm after he landed awkwardly when attacking a corner, before Sergio Busquets was shown a straight red card two minutes from time.
Puyol had just returned from a hamstring injury in the only change from the side that beat Sevilla 3-2 at the weekend and in contrast to that match Barcelona got off to the perfect start in Lisbon as Messi's fantastic driven cross was just out of the reach of Artur and Sanchez slid in to notch his first goal of the season.
Benfica were nearly back on terms immediately though as a brilliant reverse pass from Nicolas Gaitan put Lima through one-on-one with Victor Valdes - but his low effort was turned behind by the Spanish international.
However, after that warning the 2011 champions began to settle down and were in particular enjoying the rare chance of playing against a side with a high defensive line.
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Artur made a brilliant save to turn away a Messi drive that was arrowing towards the bottom corner on 22 minutes before Alexis wasted a great opportunity to double his tally as he blazed over when clean through on the goalkeeper moments later.
The Chilean was off target again seconds after the restart as he chipped the ball beyond Artur but also the beyond the post when presented with another clear sight of goal, but the visitors did not have to wait long for the crucial second goal to arrive as more great play by Messi teed up Fabregas to fire in his third goal in two games.
Valdes was then called into action to preserve the lead as he flew to his right to turn a fabulous long-range strike from Gaitan behind before Jardel could only head straight at the goalkeeper with a free header from 10 yards.
Artur then had to alert again to turn away a good downward header by Messi but the sting was taken out of the game with 15 minutes remaining when Puyol suffered his sickening looking injury. The centre-back seemed to trap his arm underneath his body as he fell to the ground and was unable to move the injured limb as he was carried from the field indicating he will almost certainly miss the El Clasico clash with Real Madrid on Sunday.
And Barca's unneeded troubles were compounded when Busquets appeared to be harshly dismissed for blocking off an opponent in what seemed like a routine challenge.