Ferran Jutgla had given Barca the lead early in the second half, but Exequiel Zeballos levelled with 15 minutes to go to take the game to a shootout.
The match, which took place at Mrsool Park in Riyadh, was arranged to honour the late Maradona, who passed away on Nov. 25 last year.
Maradona, considered one of the best players to ever play the game, played for both Barca and Boca in a professional career which ran from 1976 to 1997.
He played twice for Boca, between 1981 and 1982 and again between 1995 and 1997. He joined Barca from Boca in 1982, spending two seasons with the Spanish club before signing for Napoli.
Barca coach Xavi Hernandez took advantage of the game against the Argentine team to hand a debut to Dani Alves, who returned to the club at the age of 38 last month.
A cagey first half, in which Alves was the best player, opened up after the break, with Jutgla, a summer signing from Espanyol, opening the scoring in the 50th minute.
Philippe Coutinho handled an Alves cross but it was missed by the referee, allowing Jutgla to spin and fire in his first goal for Barca.
Ilias Akhomach and Jutgla missed chances to double Barca's lead, while Neto did well to keep out Sebastian Villa before substitute Zeballos's turned home Frank Fabra's cross to take the game to penalties.