Neymar grabbed the opener in the Group F clash at the Camp Nou 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.
Ajax briefly threatened a comeback when Anwar El Ghazi halved the deficit two minutes from time, but Sandro drove home a third in stoppage time to secure a deserved victory for the Catalans.
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.
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.
Moments later it was Messi who had a good chance to double the hosts’ advantage, but he fired over from just inside the area.
The Argentine did get on the scoresheet midway through the first half when he collected a lovely pass from Andres Iniesta and, despite Jasper Cillessen’s best efforts, Messi’s low shot trickled over the line.
Messi was the provider once more as Barca came within inches of a third when Pedro Rodriguez smacked the post.
And only a fine save from Cillessen prevented Iniesta from sealing a wonderful individual run with a goal six minutes before half-time after he ghosted past three Ajax defenders.
Messi’s goal had brought the four-time World Player of the Year level with Cristiano Ronaldo on 69 Champions League goals, two behind Raul’s all-time record of 71.
His attempts to inch closer to the record were frustrated after the break as he had a goal rightly ruled out for offside before firing into the side-netting from a narrow angle.
Neymar, Messi and Iniesta were all then withdrawn with the upcoming trip to the Bernabeu in mind, and with the major threat to their goal removed, Ajax began to create chances of their own.
Davy Klaassen blazed over when well-positioned inside the area 15 minutes from time, and Frank de Boer’s men did ensure there were a nervy final few minutes for Barca when substitute El Ghazi bundled the ball home from close range two minutes from time.
However, Sandro sealed the three points with a fine low finish into the far corner at the end of a flowing counter-attack in the fourth minute of stoppage time- AFP
