A superb goal from Benjamin Jeannot, who smashed in a sensational volley with three minutes remaining, looked to have rescued a point for Dijon on Saturday.
But Meunier, who had previously netted a second-half opener, popped up to strike again – the right-back now has seven goals for club and country already this season.
Earlier, Dani Alves hit the woodwork in one of the rare moments of quality in a quiet first half that saw Dijon restrict PSG.
And host of missed chances from Kylian Mbappe almost haunted the visitors as they failed to convert their second-half dominance into goals prior to the late drama.
PSG were not at their formidable best but now have 25 points from a possible 27 in a fine start to the domestic campaign. Dijon, meanwhile, sit 17th with only one victory from their first nine games.
Angel Di Maria - brought into the starting line-up in place of Edinson Cavani after the Uruguayan's international exploits - threatened first as his curling effort from just outside the area was pushed away by Dijon goalkeeper Baptiste Reynet.
The hosts were more than holding their own and Jordan Mane volleyed narrowly wide, before PSG keeper Alphonse Areola had to react impressively to parry away a powerful, swerving strike from Kwon Chang-hoon.
Despite a lacklustre showing in a quiet first half, PSG came close to going into the break in front, Alves sending a magnificent 30-yard free-kick dipping towards the top corner, although his effort ultimately hit the angle between post and bar.
Heroic Dijon defending denied PSG early in the second half, Julian Draxler and Mbappe both having close-range efforts kept out by last-ditch blocks from Papy Djilobodji and Oussama Haddadi.
Djilobodji then produced an overhead kick at the other end which Areola had to push wide, while Di Maria should have scored after a mistake from Reynet left him out of position, the midfielder blasting over when only Dijon defenders stood between him and the goal-line.
PSG were upping the pressure and Mbappe soon fired over from another golden chance, failing to find the target from inside the six-yard box after a great right-wing cross by Di Maria.
Reynet saved from Mbappe at the second attempt as the forward raced on to an Alves throughball shortly before PSG hit the woodwork for the second time in the match from the resulting corner, with Marquinhos heading against the bar after Neymar's delivery.
The inspired Dijon keeper saved twice more from Mbappe in PSG's next attacks, the second seeing him get down to make a key stop after Di Maria had impressively given the France international another shooting opportunity from only six yards out.
PSG finally made the breakthrough with 20 minutes remaining, Meunier beating Reynet at his near post on a rebound caused by Neymar's initial effort being saved.
But just as Unai Emery's men looked like they were successfully taking the sting out of the game, a stunning moment saw Dijon move level. A high ball from the back caused havoc between Presnel Kimpembe and Marquinhos, allowing Jeannot to send a magnificent volley over Areola and in.
PSG were not to be denied, though, with good work from Mbappe down the left teeing up Meunier's effort, which only just crossed the line as the visitors' chances of regaining their Ligue 1 crown were further strengthened.
Key Opta stats:
- PSG have won all five of their Ligue 1 encounters with Dijon: 2-0 on 23 October 2011, 2-1 on 11 March 2012, 3-0 on 20 September 2016, 3-1 on 4 February 2017 & 2-1 on Saturday.
- PSG have only lost once in their last 29 Ligue 1 games (W24, D4), against Nice on 30 April 2017.
- In addition to scoring 29 goals in nine league matches this season, PSG have hit the woodwork 11 times.