The visitors found the net 10 minutes after half time and it was enough to give them all three points as Luis Enrique's side lost for the second time in a row
The Barca coach - who arrived at Camp Nou from Celta in the close-season after the ill-fated Gerardo Martino reign - had been looking to get his side back to winning ways after their 3-1 El Clasico humbling to Real Madrid last weekend.
However, despite dominating throughout, the Catalans were ultimately left to rue missed chances as Larrivey struck in the second half to send them crashing to another potentially-costly defeat.
Luis Enrique handed a home debut to Luis Suarez following the completion of his much-publicised ban and although the Uruguayan was generally quiet, Barca still created a host of opportunities.
They hit the crossbar four times - twice each for both Neymar and Lionel Messi, the latter of whom continues to chase a record-equalling 251st La Liga goal.
Celta, by contrast, were clinical and after a mix-up in the Barcelona defence, Larrivey slotted home in the 55th minute to settle matters.
Despite Barcelona's late pressure, Celta held on to claim a memorable victory, leaving the early title tussle at the top of La Liga wide open.
Barca began the match brightly as Neymar went close twice inside the opening 15 minutes, first heading straight at Sergio Alvarez, before rattling the crossbar with an audacious effort from 25 yards.
The hosts failed to build on that early momentum, however, and gave Celta a period of respite, but they soon burst into life again in the 30th minute, with Messi unsurprisingly proving pivotal.
The Argentinian forced Sergio into a fine acrobatic save after collecting a well-placed cut-back from Neymar.
Messi then saw a goal-bound effort knocked onto the crossbar by Jonny Castro.
Barca's playmaker went close for a third time in the 34th minute, heading Suarez's left-wing cross over despite being unmarked.
Celta did well to frustrate their hosts, but it was Sergio who continued to be the hero for Eduardo Berizzo's men, denying both Messi and Neymar as the first half drew to a close.
Barca started the second half in determined fashion and they hit the crossbar for the third time just two minutes into the period, as Neymar met Jordi Alba's well-placed pass.
And Celta soon capitalised - Larrivey pouncing on uncertainty in the home defence after he had linked up with Nolito to slot past Claudio Bravo.
Luis Enrique's side almost found themselves two goals down with 12 minutes to play, as Bravo palmed away a Nolito effort and substitute Charles headed the rebound over from eight yards.
Messi then hit the woodwork again with a long-range free-kick, but Celta held on to take all three points and make it three games without defeat for them and two losses in a row for the Catalan giants, who now trail Real Madrid and Atletico Madrid in the league.