Barca was cruising at half-time thanks to Munir El Haddadi and Arthur, who put the LaLiga champion in a commanding position in Pasadena, California.
A €40million signing from Gremio, 21 year-old Brazilian midfielder Arthur curled a shot past Spurs goalkeeper Paulo Gazzaniga approaching the half-hour mark at the Rose Bowl.
Arthur's memorable strike followed Munir El Haddadi's opener 14 minutes earlier, however, Tottenham dominated the second half and scored two goals in as many minutes with 15 minutes remaining through Son Heung-min and substitute Georges-Kevin N'Koudou.
Barca, though, held its nerve in the shoot-out as debutant Malcom – who was set to join Roma before the move was controversially hijacked by the Spaniards – scored the winning penalty after Anthony Georgiou's penalty was saved.
Barca was without a number of first-team regulars, with Lionel Messi, Luis Suarez, Philippe Coutinho, Ousmane Dembele and Gerard Pique among the absentees for the club's United States tour.
The Spanish giant, however, were still able to call on Nelson Semedo, Andre Gomes and Jasper Cillessen for their ICC opener, while Clement Lenglet – signed from Sevilla – made his debut alongside Arthur.
Premier League side Tottenham, which crushed Roma 4-1 last time out, included two-goal heroes Fernando Llorente and Lucas Moura as well as Christian Eriksen, Son, Serge Aurier and Moussa Sissoko.
Barca controlled proceedings from the outset and it exposed Tottenham's high defensive line on numerous occasions before breaking the deadlock.
Munir – who spent last season on loan at Deportivo Alaves – lost his man at the back post and headed into an empty net from close range after Rafinha directed a header cross goal in the 15th minute.
Semedo was constant threat down the flank and the Barca full-back almost doubled the lead, with his fierce shot parried away for a corner.
Barca got its second goal in the 29th minute – Arthur teed up by Rafinha before unleashing an unstoppable shot into the far corner of the net – but there were concerns for the LaLiga champion after Denis Suarez and Gomes were forced off prior to the break.
It was a comfortable opening 45 minutes for back-up keeper Cillessen, who made a relatively routine save to keep out Eriksen's free-kick.
The Netherlands international was beaten seven minutes into the second half but the crossbar came to his rescue as Eriksen's long-range set-piece hit the woodwork for Spurs, who lost Sissoko to injury in the first half.
There was some desperate defending from Barca in a goal-mouth scramble with 18 minutes remaining but the ball fell to Son, who side-footed his shot into the bottom corner of the net.
Tottenham equalised within a minute after N'Koudou thumped the ball into the net after Barca's inability to clear its lines as the match headed to penalties.