The result extended the Blaugrana's lead atop the table to an unreachable 11 points over Atletico Madrid and secured a 25th Spanish first-division crown for Ernesto Valverde's outfit.
A Lionel Messi hat-trick proved the difference on the day, with captain Andres Iniesta - who announced his decision to leave the club after 16 seasons of service - enjoying a five-minute cameo and ovation at the end of the match.
This particular result also sees Deportivo join Las Palmas and Malaga in the Segunda Division next season, as Clarence Seedorf's side suffered relegation despite mounting an admirable fight against the newly-crowned champion.
Having also previously procured the Copa del Rey title, Barcelona now looks to round off its impressive campaign by defeating bitter rival Real Madrid in El Clasico on May 6, though the Blaugrana's historic enemy will not put on the traditional guard of honour that celebrates the champion of La Liga.
Instead, Zinedine Zidane's third-placed outfit will hope to spoil the party by bringing to an end Barcelona's undefeated league campaign with an away win at Camp Nou. Valverde's side has not tasted defeat in La Liga in 43 straight matches, and barring a loss in its final four matches, this would be the first instance of an "Invincibles"-style unbeaten run in the league's current format.
Adding the La Liga trophy to its cabinet alongside the Copa del Rey crown also helps mitigate this formidable outfit's listless exit from the Champions League.
Rather than focusing on the negatives, however, Valverde's players will most want to give Iniesta a proper send-off, as the 33-year-old approaches the end of his time at Barcelona.
And you can bet "Don Andres" will be in the centre of the team's celebrations, too, as the skipper claims his ninth personal La Liga title, alongside Messi.