The La Liga champions dominated proceedings in the first half at California's Rose Bowl and were two goals up at the break.
The Blaugrana added a stunning second in the 29th minute through debutant Arthur, who deftly controlled a pass from the right before unleashing a ferocious effort into the top corner from 20 yards.
Things then got worse for Spurs as they lost Moussa Sissoko on 35 minutes to what appeared to be a hamstring problem.
Spurs improved after the break, with Eriksen coming even closer from the dead ball when his free kick cannoned off the Barca post.
The breakthrough for the North Londoners came on 73 minutes, when Son Heung-min was on hand to side-foot the ball home after Eriksen's shot was saved by Cillessen.
Two minutes later Spurs were level, a scramble in the box culminating in the ball falling to Georges-Kevin N'Koudou, who made no mistake from point-blank range.
With the scores level at full time, penalties were needed to decide the outcome of the encounter.
TOTTENHAM HOTSPUR (4-4-2): Gazzaniga (Vorm 62'); Aurier, Carter-Vickers, Davies, Walker-Peters (Sanchez 46'); Amos, Sissoko (N'Koudou 35'); Son, Eriksen, Moura (Georgiou 62'); Llorente (Skipp 46')
BARCELONA (4-4-2): Cillessen; Semedo (Palencia 46'), Miranda (Cucurella 46), Marlon (Garcia 46'), Lenglet (Cuenca 46'); D Suarez (Perez 22', Tabla 70'), Roberto (Collado 46'), Gomes (Puig 26'), Rafinha (Malcom 46'); Arthur (Monchu 46'), El Haddadi (Ruiz 46')