It looked like Neymar's strike early in the second half would be enough for PSG to take all three points despite substitute Marco Verratti being sent off shortly after that goal.
But an impressive Reims side got the draw they richly deserved when Balogun broke away to fire home right at the death.
The result sees the club coached by 30-year-old Belgian-born Englishman Will Still extend their unbeaten run to 14 games between league and cup.
They remain in mid-table but have now drawn with the Parisians twice this season, their collective strength allowing a team of hungry young players to hold their own against PSG's superstars.
PSG have now dropped points in three of their four league games in 2023, and while they remain three points clear of Lens at the top of the table, their form is a concern with the first leg of their Champions League last-16 tie against Bayern Munich now little over two weeks away.
Coach Christophe Galtier fielded Lionel Messi, Kylian Mbappe and Neymar all together in his starting line-up for the first time since the World Cup as PSG took to the field wearing their fourth kit with players names in Mandarin to mark the Lunar New Year.
In fact PSG lined up in a 4-2-4 formation at the start with Carlos Soler joining the superstar attacking trio and playing on the right wing.
Yet they sorely missed Verratti in midfield with the Italian left on the bench in the first half as Reims looked the more dangerous side.
He came on at the break and they took the lead in the 51st minute as a Messi shot came off Achraf Hakimi and fell to Neymar, who duly converted his 17th goal of the season.
However, PSG were reduced to 10 men shortly after amid much confusion.
Reims were initially awarded a penalty for a foul by Marquinhos on Balogun in the box, but a VAR intervention led to the referee sending-off Verratti for a dangerous tackle on Junya Ito in the build-up and then cancelling the penalty for an offside.
PSG then saw Sergio Ramos head off the bar before Hakimi had a goal disallowed for offside.
It looked like they would hold on for the victory but, with the allotted five added minutes having been played, Kamory Doumbia sent Balogun away and the England Under-21 striker finished emphatically for his 11th Ligue 1 goal this season.