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.
However, Del Moral rose to nod in a second in the 92nd minute to preserve Sevilla's unbeaten start.
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.
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.
"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
