The Blaugrana were struggling to overcome Granada until the 32-year-old came off the bench to score the opener with just three minutes left on the clock.
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Fabregas, who returned to the Liga giants last summer having left for Arsenal in 2006, believes the Spain international is irreplaceable at Camp Nou.
“I cannot imagine Barca without Xavi,” he confessed to reporters after the match. “Someday he will [no longer be here] as with all players ever but he is a fantastic player.
“He has spent decades here at the club and is the most capped player in the club's history.”
Although Tito Vilanova’s men did not make the league clash easy on themselves - with a late own-goal swelling the scoreline in stoppage time - Fabregas insists the team are pleased with their form regardless.
“It was difficult to defend well,” the former Arsenal captain added. “We finished the game with professionalism and with patience, and we are very happy.
“We have struggled a little bit in some games, but the feelings are good.”