Spain international's wonderful set piece enough to hand Pep Guardiola's side all three points against the spirited resolve of Granada to send the champions back top of La Liga.
The win lifts the Catalans above Levante and Real Madrid to move into first place in the league, with both sides in action on Wednesday night against Real Sociedad and Villarreal, respectively.
The away team dominated possession throughout yet looked ragged in attack and had to wait until the 33rd minute to take the lead, courtesy of the Spain international's sumptuous free kick from 30 yards out.
Granada was dealt a massive blow in the 54th minute when Jaime picked up a second yellow card for a high challenge to reduce his side to 10 men. Dani Benitez also saw red for a second yellow card in stoppage time for kicking the ball away after being ruled offside.
Barcelona, which lost its100 percent Liga home record with a disappointing 0-0 draw versus Sevilla on Saturday, made a bright start in Andalusia, nearly taking the lead early on through Lionel Messi on 13 minutes. The diminutive attacker side-stepped Fran Rico before narrowly missing the target with a curling effort from the edge of the box.
The away team continued to look the stronger and came close again on 22 minutes. After a slick passing move, Dani Alves chipped a precise ball onto the head of an unmarked Pedro. However, the winger could only direct his effort wide from 12 yards.
The Blaugrana were beginning to show signs of frustration until Xavi gave them a welcome lead on 33 minutes. The captain stepped up to curl a sensational free kick over the wall, past the helpless Roberto and into the back of the net from 30 yards out - much to the delight of his adoring teammates as the away team took a lead into halftime.
Granada made a bright start to the second period but was fighting a losing battle on 54 minutes when Jaime was shown a yellow card and given his marching orders. The attacker's foot was deemed too high as he unintentionally struck Maxwell's face with his boot.
Guardiola's men thought they had doubled their lead six minutes later when Messi chipped the ball over the on-rushing Roberto, yet Diego Mainz somehow managed to get back to hook the ball to safety off the line.
In stoppage time, Dani Benitez was dismissed for his second yellow card of the game. The winger on-loan from Udinese kicked the ball away after being ruled offside, with the referee given no choice other than to show the winger a red card as Barcelona held on for the victory.
The champions will be looking for another victory on Saturday when they entertain Mallorca at Camp Nou while Granada travels to Sevilla on Monday, where it will be looking to get out of the relegation zone, and build on its solitary triumph so far this season.