Reds star Emre Can started the match and played the opening 45 minutes before being taken off at the interval.
Liverpool became the fourth club to score four or more goals against Barcelona under the stewardship of Luis Enrique.
Athletic Bilbao beat Barca 4-0 at the San Mames stadium in the Supercopa de Espana last year on 15 Augsut 2015.
Sevilla put four past Barcelona in the European Super Cup but still ended up losing 5-4.
Barca also managed to concede four against Celta Vigo losing 4-1 last year.
The La Liga champions take on Sevilla next in the Spanish Super Cup while Liverpool kick off their Premier League campaign with a clash against Arsenal.
Barcelona did end up wining the La Liga and Spanish Cup trophies last season but were unable to defend their Champions League title.