After Pique's seventh-minute opener got the Spanish champions going, Neymar used some masterful dribbling to throw off defender Efe Ambrose with his change of rhythm before cutting a pass back into the box for Pedro to direct home in the 40th.
The Brazil forward was able to tap home his first goal since Nov. 10 four minutes later after Alexis Sanchez lifted a ball over Celtic's defense to meet Marc Montoya's run, and the Spanish fullback slid it back for an easy goal.
Neymar showed no problems handling Barcelona's slick combination capabilities as he backheeled to Xavi Hernandez who returned on to his run through the defense, and Neymar sent a rising shot into the corner as he slipped to the ground in the 48th.
"I wouldn't say some players gave up but it certainly looked that way at times," said Celtic coach Neil Lennon.
"A lot of half-hearted performances and, as a manager, that was the most disappointing aspect of the whole game."
Ambrose was caught out again in the 58th. Neymar's stepover created space before he used his other foot to slide the ball through the big defender's legs, get into the box and then beat Forster.
Neymar nearly had a fourth in the 65th as he beat the offside trap to go in alone on Forster, only to dabble too long looking for a shot and his run collided with Pedro, who took a shot that was saved.
Forster could only watch as Tello, who returned from injury to replace Sanchez, tried a shot that deflected high and into goal in the 72nd minute.
"I hope, with this game tonight, that we've put to rest any doubts about our play," Pedro said.
Barcelona, which rested Andres Iniesta, rebounded from a 2-1 loss to Ajax to finish top of the standings with 13 points. AC Milan also advanced after drawing 0-0 against Ajax to finish second.
"What's important is we've overcome two straight losses and that can change things for us as we concentrate on the league," Neymar said after taking his season goal tally to seven.
