The Spain international converted the all-important winner as the Blues momentarily moved nine points clear at the top of the Premier League table.
The Torino striker scored twice as Giampiero Ventura's charges thrashed their opponents, with all four of the visitors' goals coming in the first half.
The Arsenal left-back found the back of the net for his country for the first time as Julen Lopetegui's side strolled to victory in Granada.
Last season's runners-up miss out on the chance to end the group stage with a perfect record as Carlo Ancelotti's side win at home again.
The French striker scored the winning goal late in Tuesday's game to ensure the European champions remain in with a chance of finishing top of their group.
Jordan Henderson had a hand in both goals as the Three Lions made it two wins from two in World Cup qualifying after seeing off the Group F minnows at Wembley Stadium.