Messi scored from the penalty spot at the end of the first half and added his second after the break, firing home from inside the area after receiving the ball from Javier Mascherano.
Luis Suarez had earlier equalised for Barca, who fell behind to an Eliaquim Mangala header, with the Valencia defender then sent off for a second yellow card for hauling down the Uruguayan inside the area.
Munir El Haddadi, on loan at Valencia from Barcelona, had then made it 2-2, but Messi and then Andre Gomes’ first goal for his new club sealed the three points.
“Amazing,” Luis Enrique said in his postmatch news conference when asked to once again put into words just how special Messi is.
“He’s broken all of the records and he will keep on breaking them. What a wonder to be able to enjoy him.
“His numbers are out of everyone’s reach. Messi’s numbers are impossible for anyone who is not him. We will miss them in the future.”
The Barca boss was also happy to see captain Andres Iniesta find his form again after a season which has seen him struggle with injuries.
This was the first time Iniesta had completed 90 minutes in a league game since the beginning of January and there had been doubts about his place in the side since the switch to a back three.
“It’s not a fixed thing,” Luis Enrique added of his side’s new system and Iniesta’s involvement.
“I’m sure we’ll will return to 4-3-3 at times but I think that 3-4-3 gives us some interesting variables. We could use different formations, too.
“That Andres is playing well is something to enjoy. Due to injuries he has missed a lot of games this season and now we can see the best Andres again. Now I hope he enjoys himself with the national team returns in top condition.”
Speaking after the game, which saw Barca move back to within two points of league leaders Real Madrid, Iniesta called on his side to keep racking up points in the hope that Zinedine Zidane’s side slip up.
He said: “La Liga is still alive for us, our obligation is to be prepared if an opportunity [to close the gap on Madrid] arises. We have to keep fighting in the event that a chance to take a step further arises.”