Thiago Silva opened the scoring for champions PSG before Edinson Cavani converted a penalty for his 100th goal for the club.
Belhanda's superb angled strike in the fifth minute at Guingamp was enough to hand the home side their first defeat in eight matches, as Nice overcame a recent wobble to reaffirm their title credentials.
Without injured striker Mario Balotelli, the visitors struggled to extend their lead, and were left holding on for a win that returns them to the summit on 36 points.
"We had the chance to make it 2-0, and that's what's regrettable," Nice coach Lucien Favre told reporters. "But if you can't make it 2-0, know how to hold on to 1-0...that's what we did today."
Nice are three points ahead of third-placed Monaco, who conceded a late equaliser to draw 1-1 at Dijon on Tuesday and were overtaken by PSG, now on 35 points after their 2-0 victory over Angers.
PSG's early dominance paid off when captain Thiago Silva opened the scoring in the 34th minute after leaping above the visiting defence to meet Lucas Moura's corner and send a well-directed header across goal and into the far corner of the net.
Cavani, hunting his landmark goal, was flagged offside six times before reaching his centenary in the 66th minute when he converted from the spot after Hatem Ben Arfa was brought down by Romain Thomas's clumsy challenge.
"It was an important match to win," PSG coach Unai Emery said. "For the three points, for the standings, because we were at home and because it's important to feel strong for the supporters.
"Against a difficult and defensively compact team, we had a solid, serious match and it was vital to take all three points."
Fourth-placed Olympique Lyonnais responded to their weekend defeat by PSG by demolishing hapless Nantes 6-0 away, reducing the gap to third place to eight points.
Issiaga Sylla scored the only goal of the game as eighth-placed Toulouse ended their five-game losing streak with a home win over Montpellier, while Nancy thumped Eastern rivals Metz 4-0.
Leaders Nice host Toulouse this weekend, while PSG are at Montpellier and Monaco face Bastia.
(Reporting by Ed Dove; Editing by Toby Davis)
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