Former champions Milan and Porto began the group phase with victories but last year's runners-up Borussia Dortmund suffered a jarring defeat at Napoli after being reduced to 10 men and having manager Juergen Klopp exiled to the stands.
A day after Ronaldo threw down the gauntlet with a hat-trick for Real Madrid in a 6-1 thrashing of Galatasaray, prolific Argentine Messi responded with three goals in Barcelona's 4-0 Group H romp at home to Ajax Amsterdam.
Whatever magic Ronaldo conjures, Messi always seems to have a riposte, soaring to ever greater heights in the ongoing duel between Europe's two most deadly marksmen.
Messi went through his repertoire, breaking the deadlock with a curling free kick after 22 minutes, running in his second 10 minutes into the second half and, after Gerard Pique had also got in on the act, completing his hat-trick with a clinical finish 15 minutes from time.
His latest exploits made him the first player to score four hat-tricks in the Champions League and took his overall tally to 62 goals in 80 matches in the competition.
Ronaldo, three times beaten to the World Player of the Year award by Messi in the last four years, has 53 goals in 93 games.
"We're riddled with stars and it's normal for a player to put in an excellent performance," said Barca coach Gerardo Martino after his first Champions League game in charge of the side.
"I need a solid team so that the individuals can develop their full potential," he said.
After Tuesday's torrent of 30 goals, defences tightened up in Wednesday's Group E-H games with only four goals arriving in the night's eight matches before halftime - all scored by south Americans, including Napoli's new recruit Gonzalo Higuain.
Another came from Chelsea's Brazilian Oscar as Mourinho's first European game in charge since returning to the club that fired him six years ago appeared to be going to plan.
But Basel had other ideas as Mohamed Salah curled in an equaliser before Marco Streller headed a late winner to avenge his side's Europa League semi-final loss to Chelsea last season.
"I'm not happy with the result," Mourinho said of the debacle as Chelsea suffered their first defeat in 30 home group matches in the competition.
"Instead of moving a step forward towards qualification we have taken a step back,” he said.
"Emotionally, this is not a mature team and when you are in a difficult position it was not enough," he added.