The Ligue 1 leader fell to a shock defeat as the Polish international's header ensured a famous victory for the struggling side, only its second since October.
After a first half full of chances at either end, the winning goal was scored by Gregorz Krychowiak, formerly of Bordeaux, as he headed in from a corner. Minutes before, the relegation strugglers were down to 10 men following Christopher Glombard's red card.
For all of PSG's enterprising efforts, it was distinctly limited up front, being frustrated by a superbly organized defense, as well as its own profligate finishing as Reims celebrated a famous win.
Following a week of Classique victories over arch-rival Olympique de Marseille, the visitors aimed to continue their recent good form as Zlatan Ibrahimovic and Lucas Moura combined to test Kossi Agassa in the Reims' goal early on.
Hubert Fournier's men, who before this weekend amassed only one win in 19 games in all competitions, started brightly, as Antoine Devaux forced Salvatore Sirigu into a smart save.
Carlo Ancelotti's side was at best sluggish in the opening exchanges but it was still liable for a couple of gilt-edged chances, though it should've been 1-0 down in the 35th minute when Anthony Weber's goal-bound shot was blocked, with Sirigu beaten amidst lax defending in the PSG box.
Seconds later, and PSG should've been one up. The Ligue 1 leader's signature counter-attack resulted in Ezequiel Lavezzi on a one-on-one situation against Agassa, but he fluffed his shot completely, directing the ball considerably wide as a furious Ancelotti watched on.
Ibrahimovic would have a goal wrongly chalked off for offside moments into the second half. Springing the offside trap and played on by Mohamed Fofana, the Swede produced a fine finish to beat Agassa, before a controversial offside flag scuppered his side's advantage.
PSG's task was made a little easier after the hosts saw Christopher Glombard sent off. The midfielder, playing at right back following Aissa Mandi's suspension, was shown a second yellow for a poor tackle on Matuidi, but that setback only sought to spur on Reims, which took a deserved lead.
From a corner, Fofana headed on towards the far post, allowing Poland international Krychowiak to head in unmarked, as Reims finally came good following a string of chances. David Beckham then entered the field as a 64th minute substitute, replacing Marco Verratti.
The Ligue 1 leaders failed to ignite at the other end, with further chances from Lavezzi, Matuidi and Lucas Moura all being dealt with by a resolute Reims defense as well as an inspired Agassa. It could have been 2-0 when Odair Fortes' superb run saw his goal-bound shot parried by Sirigu.
Despite a late surge in attacking intensity, Fournier's side held on in what would prove to be a champagne moment for the Champagne club.