As Barca racked up its largest win in the competition, the Argentine registered a record sixth Champions League hat-trick -- one more than Ronaldo.
However, the Portuguese's 93 Champions League goals are unsurpassed, even if Messi narrowed the gap by taking his tally to 86.
Messi needed just three minutes to rifle the opener at the Nou Camp, and he doubled the lead in Tuesday's opening Group C encounter just moments after Moussa Dembele's spot-kick was saved by home keeper Marc-Andre ter Stegen.
Neymar, who provided four assists, soon curled home a fine free-kick, Andres Iniesta lashed home a stunning volley before Messi added a fifth as Barcelona rebounded from Saturday's shock defeat to Alaves in blistering fashion.
The five-time world footballer of the year also hit a post, just seconds before setting up Luis Suarez -- whose first goal was another fine volley -- to tap home his second.
The defeat for Celtic, which won the competition in 1967, was the Scottish side's heaviest European loss.
Yet Barcelona could be punished by European football governing body UEFA after fans displayed thousands of pro-Catalan independence flags prior to kickoff.
Barca was fined $170,00 for the same offense -- such political statements are banned -- during last season's competition, with a portion of the fine suspended for two years.
Meanwhile, Ronaldo, who finished top scorer in last season's Champions League campaign with 16 goals, has the chance to pull away from Messi once again when the reigning European champion hosts Sporting Lisbon on Wednesday.
In Group A, French champion Paris Saint-Germain was held to a 1-1 draw at home by Arsenal despite dominating for large parts of the game.
Edinson Cavani headed home for the host after just one minute before proceeding to miss several chances, so allowing Alexis Sanchez to draw the Gunners level late on.
Both sides finished the match with 10 men as PSG midfielder Marco Verratti and Arsenal substitute Olivier Giroud were sent off in the 93rd minute.
Switzerland's Basel was held to a 1-1 draw at home by Ludogorets in the other Group A clash, with the Bulgarian champion taking part for only the second time.
Carlo Ancelotti has been brought in by Bayern Munich to win the Champions League and the Italian, who has done so three times as a coach, started his Group D campaign with a comprehensive 5-0 win over Russian debutant Rostov.
It proved an unforgettable night for Joshua Kimmich, 21, who scored his first two goals in the competition while Thomas Muller netted on his 27th birthday.
It was Bayern's 13th consecutive home victory in the Champions League, beating the previous best mark held by Manchester United.
Also in Group D, last season's runner-up Atletico Madrid started its campaign with a 1-0 win away to PSV Eindhoven.
In Group B, Napoli won 2-1 at Dynamo Kiev, whose goalkeeper Oleksandr Shovkovski made history by becoming the second oldest player in the Champions League at the age of 41 years and 255 days.
Marco Ballota -- formerly of Lazio -- remains the oldest at 43 years and 252 days.
Brazilian Talisca is also unlikely to forget Tuesday's action as the attacking midfielder, who is on loan at Besiktas from Benfica, scored for the Turkish side in injury time in a 1-1 draw in Portugal.
Meanwhile, Manchester City's home Group C match with Germany's Borussia Mönchengladbach was called off because of a torrential downpour.
The game will now take place on Wednesday.