Barca came into the match on the back of a defeat to Levante in the Copa del Rey, but were back to winning ways with a relatively simple victory at Camp Nou.
Erick Cabaco opened scoring for the hosts as early as the fourth minute of the encounter with Ruben Rochina claiming the assist for the goal.
And just 14 minutes later, Borja Mayoral doubled his side's lead as cruised to a 2-0 win after the first half of the encounter.
Check out our breakdown of the game below.
Messi scored his 400th league goal in his 435th appearance - the first player to reach the milestone - with Cristiano Ronaldo the only other to have scored more than 300 goals in the Spanish top flight.
Coutinho signed for Barca in January previous year 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.
Starting XI: Ter Stegen (7); Roberto (7), Pique (8), Lenglet (8), Alba (7); Rakitic (6), Busquets (6), Arthur (6), Coutinho (8); Messi (8), Suarez (9*).
He has only scored four goals in the league, and has reportedly fell out of favour with Valverde.
Suarez's second was a particularly fine goal, as he fired home at Riesgo's near post following a quickly taken throw-in.
Gerard Pique nearly opened the scoring for Blaugrana in the ninth minute after flicking Lionel Messi's free-kick at the near post but his effort missed just wide.
While talking about his team selection, Ernesto Valverde said "I picked the best team I thought we could pick", and then further added "It served us to evaluate players in some tough moments, like in a LaLiga game".