On what was a cold, windy, and wet night in Galicia, Ansu Fati broke the deadlock when he placed a calm finish into the back of the net after a scramble in the Celta box.
This seemed to spark the hosts into life and prompted both sides to take the game to one another.
Barcelona defender Gerard Pique was shown a straight red card for a last man foul on Denis Suarez in the 35th minute but replays showed that the former Blaugrana midfielder was offside, sparing Pique's blushes.
His defensive partner Clement Lenglet was not so lucky and after two clumsy challenges, referee Carlos Del Cerro gave him his marching orders for two bookable offenses.
Barcelona manager Ronald Koeman had to sacrifice Antoine Griezmann to shore up his defence, with the Frenchman being replaced by Ronald Araujo right on the stroke of half time.
The second half begun in the best possible fashion for the visitors as Lionel Messi and Coutinho combined brilliantly, before the Argentine's cutback into the area was deflected into his own net by Lucas Olaza.
From then on, it was cruise control for the Catalans and despite being a man down, they never looked like relinquishing their lead and threatened to add a few more goals.
Sergi Roberto made it 3-0 with virtually the last kick of the game after Messi's goalbound shot was deflected into his path. The Spain international made no mistake from 16 yards out, rifling into the top corner to put some gloss on the scoreline.
The victory takes Barcelona up to 5th on the standings and here, we shall have a rundown of five talking points from the fixture.
#5 Ronald Koeman era getting into full swing
It is no hidden secret that the last season was arguably the worst in Barcelona's long and illustrious history, with the debilitating 8-2 whitewash by Bayern Munich in the Champions League marking the nadir.
Wholesale changes were needed across the board and former manager Quique Setien was sacked to be replaced by Ronald Koeman.
The Dutchman could not have arrived in more dire circumstances as just few days after his appointment, the club was rocked by the news that captain and talisman Lionel Messi wanted to depart the club.
The sale of key players including Luis Suarez, Arturo Vidal and Ivan Rakitic also threatened to derail the season, and many were already calling for Koeman's head before a ball was even kicked.
After all the off-field hullabaloo died down, attention turned to matters on the field, and the Barcelona manager could not have asked for a better start by his side.
The fixture list showed that the Blaugrana had to face Villarreal, Celta Vigo and Sevilla in their opening three league fixtures, and the Catalans have kicked off the campaign in impressive fashion.
Villarreal and Celta Vigo were dispatched with ease in 4-0 and 3-0 victories respectively. Considering that both clubs were expected to give Barcelona a sterner test, it makes the results all the more impressive.
Coming into this game, the Catalans had not won at Celta for six years but that counted for nothing, and they put up a dominant performance to pick up all three points.
It might still be early days in the season but Ronald Koeman has started his Barcelona tenure brilliantly.
Two games, six points, seven goals, two clean sheets, Philippe Coutinho looks comfortable; there is hardly much more that fans of the cub could have asked for.
#4 Fantastic Fati continues upward trajectory for Barcelona
Just under a year ago, Ansu Fati announced himself to the world when he became the youngest league goalscorer in Barcelona's history and since then, the 17-year-old has set records tumbling faster than you could say Jack Robinson.
Having grabbed a brace in the 4-0 victory over Villarreal, Fati was at it again and opened the scoring with an excellent finish. His presence of mind to use the outside of his boot to score the goal while under the attention of two defenders belies his age.
The goal took him to three goals for the season from just two matches and at this rate, fans of Barcelona would be confident of their future post-Messi.