Neymar grabbed the opener in the Group F clash at the Camp Nou on Tuesday after just seven minutes when he collected Messi's pass to curl the ball into the far corner before Messi put Barca firmly in command when he slotted home 14 minutes later.
Barca coach Luis Enrique then withdrew Neymar, Messi and Andres Iniesta in the second half to keep them fresh for the weekend.
Edinson Cavani's late winner for Paris Saint-Germain away to APOEL Nicosia means Barca remain a point behind the French champions at the top of Group F, but extend their advantage over third-placed Ajax to four points.
"We didn't kill the game in the first half when we were well on top and then after a scramble they get back into the game," said Luis Enrique.
More From This Section
"But I am happy with what I saw on the field. We are going to the Bernabeu at a perfect time. We are leaders in the league and are desperate to measure ourselves against our eternal rivals."
"I think we gave them too much respect. I know we don't have much experience in the team but playing against a team of this level you can't give them that much respect.
"I can understand it, but at the same time you dream of playing these games so you have to show your quality."
Messi and Neymar have now combined for 19 of their side's 28 goals this season and the lethal duo combined to open the scoring as Messi sucked in the Ajax defence before releasing Neymar to curl home his 10th goal in as many games.