Remy Cabella's second-half goal cancelled out Maxwell's superb opener in the 37th minute for PSG, who had France centre back Sakho sent off after nine minutes.
The Qatari-backed club are top the table on 23 points from 12 games, ahead on goal difference of Olympique Marseille, who let a winning position slip for the second time this week in a 2-2 home draw with Nice.
Montpellier, also reduced to 10 after Younes Belhanda was shown a second yellow card midway through the second half, are 14th on 13 points.
The champions dominated possession from the start without posing a threat to well-organised PSG, whose plans were ruined when Sakho was dismissed after he pulled Gaetan Charbonnier's shirt while the striker was running through the goal.
Though frontman Guillaume Hoarau - starting his first league game of the season with Zlatan Ibrahimovic suspended - was replaced after 12 minutes by centre back Alex, PSG had the best chances thanks to Jeremy Menez who set up Maxwell for a splendid lobbed goal on 37 minutes.
The France winger, who a constant menace for the Montpellier defence, was denied a second goal by keeper Geoffrey Jourdren on the stroke of half-time.
Montpellier pushed harder after the break through Cabella whose curled effort went narrowly wide in the 56th minute. Three minutes later, the young forward took advantage from a Blaise Matuidi mistake to fire into the bottom corner of the net.
Earlier, Fabrice Abriel volleyed home from close range two minutes from time to give Nice a 2-2 equaliser against Marseille. Marseille were again left regretting a late goal following their 2-2 stoppage-time draw with Borussia Monchengladbach in the Europa League game on Thursday.
"It is very disappointing, we had a lot of chances but we were not efficient enough," Marseille centre-back Nicolas Nkoulou said.
"We have taken a blow with this result. We clearly lost two points today."
The hosts started strongly and were rewarded when Andre Ayew headed home from a neat Mathieu Valbuena cross in the 40th minute.
They wasted numerous chances in the first half including a Valbuena penalty after 28 minutes when Nice goalkeeper David Ospina parried the attempt to safety.
Nice fought back early in the second half and Dario Cvitanich broke through as he headed in a Jonathan Eysseric free-kick six minutes after the restart.
Marseille went back in front when Valbuena tapped in from close range after 68 minutes and they were heading for their fourth home league success of the season until substitute Abriel snatched a point for Nice who moved up to 15th on 13 points.
At Sochaux, clinical Lyon went ahead in the 24th minute when Maxime Gonalons converted the only clear-cut chance of the first half by heading home a Steed Malbranque free-kick.
The hosts had a couple of efforts on target but goalkeeper Remy Vercoutre proved unbeatable until Sloan Privat ran onto a Ryad Boudebouz cross to net a deserved equaliser with 19 minutes left on the clock.
Girondins Bordeaux thrashed Lorient 4-0 away to move up to sixth on 21 points, Brazilian forward Jussie scoring the opener and setting up two other goals.