Ander Barrenetxea pulled one back for the hosts in the 77th minute through a fantastic volley but it proved to be nothing more than a consolation.
Following a slow start, Griezmann and Dest gave the Catalans a 2-0 cushion by the break and then ran riot in the second-half.
They hit all the right notes and tore Sociedad asunder with a frightening attacking display never seen from them until now in this campaign.
The resounding victory takes them above Real Madrid in the table and they remain just four points behind runaway leaders Atletico Madrid.
Barcelona player ratings:
Marc-Andre ter Stegen - 7/10
He was having a comfortable evening and was on his way to another clean sheet. But a golazo from Barrenetxea put a small taint on his pristine copybook.
Oscar Mingueza - 6/10
A solid shift from the Spaniard, who also made his presence felt in attacking areas by throwing his weight around in Sociedad's half. However, when they upped the ante after the break, Mingueza was a peripheral figure.
Frenkie de Jong - 6/10
He played his role as a centre-back to a T once again and made a few good blocks in the first-half to keep La Real at bay.
Clement Lenglet - 6/10
Lenglet was rock solid in defense, winning all his aerial duels. He completed 92% of his passes and two out of three tackles too.
Sergino Dest - 8/10
The young American bagged his first pair of La Liga goals in an amazing offensive display, with both strikes being top-notch.
Sergio Busquets - 7/10
Busquets played his role of orchestrator to perfection. He capped it off with a beautiful assist for Messi too.
Pedri - 6/10
Compared to how rampant everyone around him was, Pedri was a little subdued, but nevertheless attempted one shot of his own too. He ought to do more though.
Jordi Alba - 7.5/10
It was a vintage performance from the Barcelona veteran; a well-spring of excellent crosses and one assist to show for his efforts too.
Lionel Messi - 10/10
The Barcelona ace weaved his magic once again and Sociedad were left absolutely spellbound. He was involved in both first-half goals, even assisting Dest with a sublime through-ball. He then found the net himself twice after the break. Lionel Messi was at his unplayable best.
Antoine Griezmann - 7/10
Back at his old stomping ground and on the scoresheet against his old colleagues - how poetic! Griezmann latched on to a loose ball from Dembele's initial effort and opened the scoring. Co-incidentally, it was his birthday too! Not a bad way to celebrate.
Ousmane Dembele - 7/10
A constant source of threat for La Real with his great link-up play and incisive passes. Dembele topped his performance with a sublime goal.
Ronald Araujo - 6/10
Araujo replaced Busquets and helped take control of the midfield.
Francisco Trincao - 7/10
Trincao played a neat one-two with Alba to set up Messi's second goal.
Ilaix Moriba - 7/10
He picked up another assist by sending a simple offload to Dembele.
Riqui Puig - N/A
He came on for Griezmann during the final few minutes to see out the game.
Martin Braithwaite - N/A
He too came on too late and thereby saw very little of the ball.