Elsewhere, Manchester City could only manage a 1-1 draw away to Borussia Moenchengladbach
Celtic couldn't manage to draw on the memories of previous famous nights in Europe as they slumped to a 2-0 defeat at home to Catalan giants Barcelona.
Brendan Rodgers was yesterday asked if it was more difficult to believe if the Loch Ness monster exists, or Lionel Messi. He simply laughed off the question, but the smile was very much rubbed off his face as the little Argentinian scored both goals at Park Head.
The Bhoys made a promising start to the game as they pressed the La Liga champions all over the pitch, Scott Brown in particular was exceptional in the middle of the park.
The visitors made the breakthrough on 25 minutes when Neymar lifted the ball over the Celtic defence and Messi drilled the ball home at the near post.
Messi's goal pic.twitter.com/jReKD6yCGb— ️️️️barca (@cuIegirI) November 23, 2016
The second half offered little in the way of change for Celtic and Rodgers' side failed to take their chances when presented to them. Moussa Dembélé should have put the side level with a header from seven yards but it was directed straight at Marc-André ter Stegen.
Barcelona went up the other end and won a penalty, which Messi stepped up and duly converted to keep them top of Group C.
Elsewhere in the group, Manchester City could only manage a 1-1 draw away to German side Borussia Moenchengladbach. The home side took the lead through Raffael, before David Silva drew level on the stroke of half time.
There were two red cards in the second half - both for two bookable offences - as Lars Stindl and then Fernandinho were sent for early baths.
Arsenal missed their chance to go top of Group A after letting a 2-1 lead slip in the final quarter of the game. They trailed through Edinson Cavani's opener but Olivier Giroud levelled things from the spot just before the break.
Olivier Giroud levels things up from the spot against PSG. Image: John Walton EMPICS Sport
In the second half, tow own goals - one from Marco Verratti and one from Alex Iwobi - were enough to see the side finish the game level at 2-2.
2009 - Arsenal v PSG is the first Champions League match to have more goals than shots on target since Rangers v Unirea in Oct 2009. Quirky.— OptaJoe (@OptaJoe) November 23, 2016
French duo Antoine Griezmann and Kevin Gameiro got the goals for Atletico Madrid as they enjoyed a 2-0 home victory over Dutch side PSV.
There were scoreless draws between Ludogorets and Basel and between Napoli and Dynamo Kyiv.
Earlier this evening, FK Rostov produced the shock of the day with a 3-2 victory at home to German giants Bayern Munich.
Benfica and Besiktas played out a 3-3 in the day's only other game.