The 20-year-old forward scored the winner from close range one minute from time after having come on for Pierre-Alain Frau, who had opened the scoring for the visitors early in the first half.
Stade Rennes, who are ninth on 37 points, equalised midway through the first half through Jerome Leroy.
Champions Bordeaux did not play this weekend as the French League agreed to postpone their game against Auxerre to give them a break before Tuesday's Champions League last-16 first leg at Olympiakos.
"We got off to a good start and we scored quite early in the game thanks to Michel Bastos, who showed great efficiency in front of the goal and performed very well in the first half," Lyon coach Claude Puel told Foot+ channel.
"We controlled the pace of the game after the break as we were a little bit tired," he added, referring to Tuesday's 1-0 win against Real Madrid in the Champions League.
"I don't mind who scores. The most important thing was to beat Nancy... If I'm Ligue 1 top scorer at the end of the season, it will only be the ice on the cake," Niang told reporters after his 14th goal of the campaign took him to the top of the scoring charts.
Marseille captain Niang headed home his side's first goal at the near post from a cross by Charles Kabore in the 10th minute.
Nancy's Andre Luiz scored an equaliser from close range three minutes later but Niang put the home side in front again with a left-footed volley from inside the box just after the half hour.
Niang sealed Marseille's win after the break following a swift counter-attack.
