The 31-year-old Spain midfielder, playing his 392nd league match, struck in the 33rd minute at Granada's Los Carmenes stadium to lift the champions above surprise packages Levante and great rivals Real Madrid to the top of the standings.
Xavi's mark beat the previous record set by Migueli, a central defender known as "Tarzan" who played for Barca in the 1970s and 80s. Xavi already owned the appearance record for all competitions, which he extended on Tuesday to 591.
"It was a difficult match that we were unable to kill off in the second half," he told reporters after scoring his fourth league goal of the campaign.
"Generally it was a good performance but everything can be improved on," he added.
Barca, who have not conceded a goal in seven matches in all competitions, have 21 points from nine games. Levante are on 20 from eight ahead of their home match against Real Sociedad on Wednesday, when Real, who have 19 points, host Villarreal.
Sevilla stayed fourth on 17 points after they needed a stoppage-time equaliser to rescue a 2-2 draw at home to struggling Racing Santander in the late kick-off.
A 37th-minute Manu del Moral header put the Andalusians in front before second-half goals from forward Ariel Nahuelpan and youth team midfielder Jairo Samperio took Santander within sight of their first win of the season.
However, Del Moral rose to nod in a second in the 92nd minute to preserve Sevilla's unbeaten start.
FRUSTRATING NIGHT
Barca, the European champions, travelled to Granada having slipped from first to third following Saturday's 0-0 draw at home to Sevilla when World Player of the Year Lionel Messi had a stoppage-time penalty saved.
The Argentine, enduring another frustrating night, had a dinked effort cleared off the line on the hour.
The La Liga joint top scorer, level on 10 goals with Real forward Cristiano Ronaldo, has failed to score in five away games in the league for the first time since December 2009.
Granada played most of the second half with 10 men after midfielder Jaime Romero was shown a second yellow card eight minutes after the break for catching Maxwell with a high foot.
Forward Dani Benitez was dismissed in stoppage-time when he earned a second yellow for kicking the ball away.
Despite their numerical advantage, Barca were unable to add to Xavi's fine effort and even endured nervous moments in the final stages as Granada pressed for an equaliser.
Referee Cesar Muniz Fernandez brandished his yellow card 11 times, seven to Granada, who did not manage a shot on target, and four to Barca.
"We were not very quick in passing the ball around," Barca coach Pep Guardiola said at a news conference.
"When you are only 1-0 ahead anything can happen," he added. "Any lapse in concentration against s
