Despite the game being their first of pre-season, Barcelona began on top with Oriol Busquets sending a free header off target within 90 seconds of kickoff, although Chelsea also threatened with Cesar Azpilicueta heading wide at the back post.
Antoine Griezmann - on his first appearance for Barcelona since signing from Atletico Madrid - had plenty of touches during the opening quarter, and the Frenchman needed to shake off a knock to his knee after a 50-50 challenge with Jorginho on the halfway line.
Chelsea should have gone ahead in the 23rd minute through Abraham, who seemed perfectly placed to convert the rebound after a Christian Pulisic shot had been saved, but the forward somehow fired over the crossbar from six yards out.
However, soon after Mason Mount had sent an effort over the crossbar, Chelsea deservedly went in front thanks to Abraham, who superbly took the ball around Marc Andre ter Stegen before converting into an empty net.
Pulisic squandered another opportunity, this time firing into the side-netting from an acute angle, but Barcelona could have been level before the break, only for Ousmane Dembele to fire too close to Kepa Arrizabalaga from the edge of the penalty area.
Lampard refrained from making mass alterations at half time with just two changes being made, although 11 fresh faces for Barcelona meant that the Blues were outworked during the opening stages after the restart.
However, a second and match-clinching goal arrived with nine minutes remaining as Barkley drilled a left-footed strike into the bottom corner of the goalkeeper's net from 20 yards out.
Lampard would have been eager to see his backline keep a clean sheet having conceded late in two of their previous friendlies, although there was little that Arrizabalaga could do to keep out Rakitic's stunning 25-yard effort which found the top corner in the first minute of added-on time.
BARCELONA (4-3-3): Ter Stegen (Neto 46'); Roberto (Semedo 46'), Pique (Todibo 46'), Umtiti (Lenglet 46'), Alba (Jaime 46'); Oriol Busquets (Rafinha 46'), Sergio Busquets (Alena 46'), Puig (Rakitic 46'); Collado (De Jong 46'), Griezmann (Malcom 46'), Dembele (Perez 46')
CHELSEA (4-2-3-1): Arrizabalaga; Azpilicueta (Zappacosta 70'), Christensen (Tomori 48'), Luiz (Zouma 46'), Palmieri (Alonso 46'); Jorginho (Drinkwater 70'), Kovacic (Bakayoko 70'); Pedro (Batshuayi 70'), Mount (Barkley 60'), Pulisic (Kenedy 60'); Abraham (Giroud 60')