The Argentine maestro took his tally in Europe's premier club competition to 74 goals with a treble in the 4-0 victory over Cypriot club APOEL Nicosia, surpassing Raul's former record of 71 goals.
The hat-trick was Messi's fifth in the Champions League, also a record, and helped the Catalan giants record their fourth victory in Group F which has them sitting second behind French champions Paris Saint-Germain.
Despite having one player less, Pep Guardiola's went into the half-time break with a 2-1 lead thanks to goals from Xabi Alonso - a low free-kick from outside the area - and Robert Lewandowski who pulled off a classy looping header just before the break.
Just as it appeared as the Bavarian behemoth would grab their fifth win of the group stage campaign, City hit on the break in the 85th minute with Stevan Jovetic feeding Aguero who advanced into the area before slotting across Neuer with his left foot.
The City striker then dispossessed Jerome Boateng in injury-time to produce a theatrical winner which has the reigning Premier League champions sitting equal second on the Group E table with Roma and CSKA Moscow on five points after their 1-1 draw in Russia while Bayern sit seven clear on top.
In Group G, Chelsea secured top spot with a clinical 5-0 victory over Schalke in Gelsenkirchen to continue their brilliant start to the campaign.
Elsewhere, Edinson Cavani scored twice to lead PSG to a 3-1 home win over Ajax, FC Porto easily accounted for BATE Borisov 3-0 in Belarus to remain top of Group H ahead of Shakhtar Donetsk who had already qualified for the next stage despite a 1-0 home defeat to Athletic Bilbao.
And in the other Group G fixture, Sporting Lisbon moved to second with a 3-1 triumph over NK Maribor in Portugal.
2014/15 UEFA Champions League - group stage scores
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