Messi struck twice in the second half, bringing up 600 Barca goals in the process, to leave his side in a commanding position heading into next week's semifinal second leg at Anfield.
But Barca's win was tainted by the treatment former Liverpool playmaker Coutinho received when he was replaced by Nelson Semedo just before the hour mark. The club's record signing endured a difficult night against his ex-teammates but Messi didn't believe his performance was deserving of the whistles aimed at him by his own fans.
The Argentina international even celebrated his first goal -- which made it 2-0 in the 75th minute following Luis Suarez's opener -- by telling the home supporters not to whistle their own players.
Barcelona player ratings: Messi a perfect '10' in big win
"We're at the defining stage of the season and we have to be more united than ever," Messi told reporters after the game. "I said that at the start of the season. It's not the time to criticise anyone.
"We have to support each other and stick together for the rest of the season. It is ugly to treat a player like that when they're taken off."
While Coutinho's Camp Nou struggles endured, it was another electric performance from Messi, 14 years to the day since he scored his first goal for the club against Albacete. His second goal was a sublime free kick from 30 yards.
He now has 12 goals in Europe this season and 48 in all competitions, with Barcelona on the verge of a first Champions League final since 2015 and with a treble in their sights. They've already won La Liga and have a Copa del Rey final to come against Valencia later this month.
However, the scoreline did flatter Barca slightly. Liverpool had their chances throughout the game, with Marc-Andre ter Stegen making three good stops and Mohamed Salah missing a great late opportunity to grab an away goal when he struck the woodwork.
"We're not used to not having the ball and we struggled a little," Messi admitted. "But that's how the game went and we had to find a way through in whatever way necessary. They didn't manage to score and that's important.
"We were better in the first half and they pressed well in the second, but they didn't have too many chances. Of course, they wanted to get a goal, an away goal is huge. We have a good advantage but we know it's not over. Anfield's a really tough place to go."
Coach Ernesto Valverde also warned that the tie is far from over. Barca were knocked out in the quarterfinals last season by Roma when, despite winning the first leg 4-1, they were beaten 3-0 at the Olimpico.
"Liverpool had some clear chances -- one off the post," Valverde said in his postgame news conference. "And there was a great save by [Ter Stegen]. They had their moments and we had to suffer at times but, in the end, we got a good result against a really strong team.
"But it's a similar result to last year. We also had a three-goal lead against Roma."