The previous mark has been held by former Athletic Bilbao striker Telmo Zarra since 1955, which marked the end of the Spaniard's 15-year career with the Basque club.
Zarra scored his 251 goals in 277 appearances while Argentina captain Messi needed 289 games.
"We are all very happy and of course also for Leo," Barca captain Xavi told reporters.
"He has achieved an amazing and historic record," added the decorated former Spain international.
Messi, 27, equalled the record in the 21st minute with a typically breathtaking effort, curling a left-footed free kick around the wall and past Sevilla goalkeeper Beto.
He struck again from close range in the 72nd minute and scored a third goal six minutes later with a powerful low drive from the edge of the penalty area.
Messi's team mates picked him up and threw him into the air several times while his adoring fans at the Nou Camp wildly cheered their talisman who joined the club's academy at the age of 13.
The four-times World Player of the Year has scored 206 goals with his favoured left foot, 38 with his right, eight with his head and one, which should have been ruled out, with his hand.
Messi also matched former Real Madrid and Schalke 04 forward Raul's Champions League record of 71 goals last month.
(Writing by Iain Rogers in Madrid, editing by Ken Ferris)
