Gerard Pique stabbed home with seven minutes on the clock and, with Celtic stretched at the back, Pedro and Neymar both finished clinically before half-time. (Agencies)
Neymar had never scored before in Europe but got two more after the break, with Adam Matthews unable to stop the Brazilian's third from going over the line. Cristian Tello completed Barca's scoring with another deflected shot.
Celtic grabbed a consolation goal through Giorgios Samaras two minutes from time.
Barcelona finish top of the section with 13 points, four ahead of second-placed Milan and five ahead of Ajax, who drew 0-0 at the San Siro.
Barca's 20-match unbeaten start to the season was ended at Ajax in their previous European match, and it was followed by defeat in La Liga by Athletic Bilbao. But Gerardo Martino's side, still without the injured Lionel Messi, responded with a fine attacking display against the Scottish champions.
For Celtic it is the end of a poor run in Europe. They have lost all their away games, and at home, where they are normally strong, they managed only one win, over Ajax.
"It was our most complete performance, I would say, in the four months that I have been here," Martino told a news conference.
"We managed the ball well and had a good game. We were strong in winning the ball back and pressured especially in attack, while we didn't give the opposition chances.
"Neymar improved as the game went on. He has been playing wide for us and then to be moved to the centre meant he needed time to adapt, but the goals came and his confidence grew.
"All through his career you can see the quality he has, but what has surprised me here is how hard he works for the team and battles hard."
Celtic manager Neil Lennon was furious with his players.
"Barca were fantastic, as expected, but some of the performances from our players were unacceptable," he said. "It was not similar to recent performances against Barcelona. We showed no bravery and we were hesitant.
"I tried moving to a 4-5-1 (formation) to play more defensively but we were weak and it isn't nice for me to say but it is something I need to address.
"Most of the players were very poor and were below the standards we have set in recent years. I am angry and disappointed but it is something that we need to get over.
"It is very tough to take and we need to do better, analyse what went wrong. The character wasn't good enough. We started off with loose passes and we didn't play to our strengths, some players gave up and as a manager that is the most disappointing aspect."
Youngster Sergi Roberto was the surprise face in the Barcelona lineup with Andres Iniesta, carrying a knock, left on the bench. Scott Brown returned for the visitors after serving his ban for his red card for a foul on Neymar when the sides met in Glasgow.
The visitors gave Roberto the perfect opportunity to find his feet as they left large holes in the centre of midfield for the home side to carve openings.
Xavi sent a deep ball to Neymar at the far post that was just too high for the Brazilian before two minutes had passed.
Pique was getting forward well and he was on hand to get the opening goal as he knocked the ball in from close range after a deflected shot from Alexis Sanchez was saved by the keeper.
Barcelona continued to threaten but further goals didn't come until the run-up to half time, when Neymar set up Pedro to steer the ball home and then scored himself from a pass by full-back Martin Montoya.
In the second half Neymar combined well with Xavi before firing home and showed real quality to complete his hat-trick as he nutmegged Efe Ambrose. Substitute Tello completed Celtic's misery with a deflected strike off Virgil van Dijk.
Gerard Pique stabbed home with seven minutes on the clock and, with Celtic stretched at the back, Pedro and Neymar both finished clinically before half-time.