It was another remarkable milestone for Messi, who has been the league's leading scorer since 2014, with Cristiano Ronaldo next on the list with 311 goals.
Coutinho signed for Barca in January a year ago and was cup-tied in the Champions League, but he impressed in the second half of the campaign at Camp Nou, scoring 10 goals in 22 appearances as Barca won LaLiga and the Copa del Rey.
Coutinho has had his critics this season, but the Brazilian was named in the starting XI by Ernesto Valverde and repaid the faith by playing a key role in the Catalan giants making the breakthrough.
"His numbers are stratospheric, incredible".
Luis Suarez grabbed the lead for Barça in the 19th minute with a curling finish following a through ball from Philippe Coutinho, 1-0. The Argentine did the rest by opening an angle around a defender and driving in a low left-footed shot.
He has scored six goals from 23 appearances in all competitions so far this campaign but has been heavily criticised by some quarters at the club. "Once we scored, the game opened up for us" said Suarez.
Manchester United have been linked with a lot of players in the winter transfer window.
He said: "Personally, I see it hard for him to return, but in football I've seen a hundred thousand things".
Griezmann ensured that Atletico stayed in touch with Barcelona.
Having already won four trophies in 18 months in the French capital Neymar has enjoyed no shortage of success but continues to have an emotional attachment to Barca - with his first demand to return allegedly coming as early as last season.
Elsewhere, Inaki Williams struck in either half as improving Athletic Bilbao beat third-placed Sevilla 2-0 at San Mames.
Santiago Solari's side had the final say with Dani Ceballos - who was a 2017 signing from Betis - scoring in the 88th minute to leave Madrid 10 points behind Barca.