Boga picked his spot from the edge of the box, unleashing a low strike that Reims goalkeeper Yehvann Diouf palmed into his own net in the 82nd minute.
The home side had opened the scoring shortly after halftime, benefiting from an uncharacteristic long clearance from keeper Marcin Bulka which fell to Gaetan Laborde, who fired home off the underside of the bar.
Reims captain Yunis Abdelhamid met a cross from Junya Ito to equalise in the 78th minute.
"We were a bit too excited sometimes," Nice defender Dante told broadcaster Amazon Prime Video.
"We will have to correct that for the next games so that we can have more control."
Nice have built their success on solid defence this season, the stingiest in Europe's top five leagues, with only six goals conceded in 15 league games.
Ten-man Marseille earned their first league win on the road this season by beating Lorient 4-2 to move into sixth on the ladder.
Chancel Mbemba gave Marseille the lead in the third minute by pouncing on a loose ball to score from close range.
Pierre-Emerick Aubameyang continued his hot run of form by netting in his fourth straight game before defender Leonardo Balerdi made it 3-0 with a header from a corner in the 33rd minute.
Lorient winger Romain Faivre pulled one back with a half-volley shortly before halftime, but moments later Aubameyang restored Marseille's three-goal lead by beating goalkeeper Yvon Mvogo after a swift counterattack.
Marseille's intensity dropped in the second half and former Manchester City defender Benjamin Mendy scored his first goal for Lorient by firing home in the 52nd minute.
Marseille finished the game with 10 men after defender Jonathan Clauss was sent off for a high boot late on.
Lille stayed fourth by stretching their unbeaten run to nine games in the league with a 0-0 draw at Clermont.
Brest edged Metz 1-0 with a goal from substitute Jeremy Le Douaron to climb to fifth place, two points behind Lille.
Alexandre Lacazette notched three poacher's goals to snap a six-game scoring drought as bottom side Lyon thrashed Toulouse 3-0.
It was a first win for Lyon caretaker Pierre Sage who replaced coach Fabio Grosso on November 30.
Abakar Sylla headed home a corner in the last second of stoppage time as Strasbourg snatched a 2-1 win over Le Havre.
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