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Andre's hat-trick took him to 10 for the season - it was Jordan's first - and put Marseille one point ahead of long-time leaders Lille with six matches remaining and came just days after they won the League Cup.
"Not everything was perfect but its rare to score four goals so that is welcome," said Marseille coach Didier Deschamps.
"We had a difficult first-half but improved in the second, like it was a second wind.
"I am delighted by the Ayew brothers. Andre I knew had a lot of qualities but Jordan is younger and less experienced but he showed his qualities this evening which is good as I don't have many strikers."
Seven-time champions Lyon also kept alive their hopes of a first trophy in three years as they edged beaten League Cup finalists Montpellier 3-2 - France playmaker Yoann Gourcuff, who had only started on the bench, delivering the late winner.
Lyon are in third, five points behind Marseille.
Marseille had taken the lead just before the half-hour mark as 21-year-old Andre profited from an error by Nice's Colombian 'keeper David Ospina, who dropped an easy take from a Marseille corner, and the son of former Africa player of the year Abdei Pele pounced to rifle the ball home for his eighth of the season.
However, the hosts deserved an equaliser and it duly came shortly before half-time as Marseille failed to clear a corner and Abdou Traore was on hand to react fastest and shoot past Steve Mandanda from close range.
Nice thought they should have had a penalty in the 57th minute as Traore looked like he had been brought down by Mandanda but to the astonishment of the visiting players and coaching staff alike the referee Laurent Duhamel refused to give it.
At that point Deschamps decided to send on Argentinian star Lucho and Jordan to add some fresh legs.
Within two minutes it proved an inspiring decision as Jordan crossed and his brother was on hand to put the ball into the far corner of the goal.
Jordan turned from provider to goalscorer in the 79th minute as the 19-year-old scored a dream of a goal - a right-footed curling effort from outside the box which left Ospina transfixed.
"I was thinking of passing the ball instead but I took the risk and it paid off!" grinned Jordan.
Mandanda then produced heroics of his own as he got down well to save Habib Bamogo's penalty five minutes from the final whistle.
Marseille rammed home their superiority in the dying minutes as Andre rose magnificently to head home for his hat-trick - Nice's Argentinian defender Renato Civelli scored a consolation goal in time added on.
"I am really happy for my brother (Jordan) and delighted for myself but more importantly this is three points, we are top and we have our destiny in our hands," said Andre.
Lyon had taken the lead at home to Montpellier with a stunning effort from Ederson - who was playing instead of Gourcuff - in the 22nd minute as he cut in from the left and fired in a rasping swerving effort that goalkeeper Geoffrey Jourdren could only help into the net.
However, the hosts were unable to hold onto their lead for long as six minutes later Montpellier levelled, the impressive Olivier Giroud running onto a deflected pass to slot the ball under Hugo Lloris's body.
Lyon took advantage of this let off as they regained the lead in the 55th minute, Bafetembi Gomis passing unselfishly to Lisandro inside the penalty area and the Argentinian made no mistake.
Substitute Souleymane Camara levelled again but Gourcuff popped up to tuck away the decisive goal and provoke coach Claude Puel to leap from his seat and jump up and down with joy.