The German hosts twice found an equalizer in the first half before Denis Thomalla and a late own goal from Marquinhos condemned Laurent Blanc's men to a 4-2 loss.
Laurent Blanc's men twice took the lead in the first half, through Hervin Ongenda and Jean-Christophe Bahebeck, but were ultimately punished for some sloppy defending.
Boyd and Yussuf Poulsen each found equalizers for the host, which duly prevailed courtesy of a 65th minute volley from Denis Thomalla and Marquinhos' subsequent own goal.
In front of a healthy crowd in Leipzig, the host - which is preparing to play in Germany's second tier this season for the first time - more than played its part in an open first period.
However, an unmarked Ongenda was left with a simple finish to open the scoring after 10 minutes, having been picked out by Clement Chantome's square ball.
Boyd replied from close range after Nicolas Douchez had made a fine save to keep out Joshua Kimmich's initial header, but PSG - with Zlatan Ibrahimovic featuring from the start - took the lead back almost immediately as Bahebeck beat goalkeeper Fabio Coltorti to head home a cross from Ongenda.
Ibrahimovic was guilty of a poor miss before Poulsen converted a right-wing corner six minutes after the interval to make it 2-2.
Leipzig then moved in front, Thomalla capitalizing on more generosity from PSG's back line, and Marquinhos deflected substitute Stefan Hierlander's effort past his own goalkeeper as Leipzig claimed a notable scalp.
PSG takes on Kitchee next in Hong Kong on July 29.
Boyd, 23, joined the newly promoted 2.Bundesliga club this offseason from Rapid Vienna. Today's tally is his second during the club's preseason,