Both sides came into the game with similar unbeaten records, and it was the home side who started off stronger as Badredine Bouanani whipped a superb effort that flew inches wide with Jack Butland beaten.
The Rangers shot-stopper was called into action once again in the opening quarter-hour before John Souttar cleared his lines. From that moment on, the Scottish outfit dominated the remainder of the first half.
That domination produced a goal rush from the 35th minute onwards as Rangers went into the break with a stunning 3-0 lead.
The first goal arrived via Vaclav Cerny’s drilled effort just inside the box, and less than three minutes later, the second came as a result of some dreadful defending from the Nice backline, which allowed Mohamed Diomande to race through and poke home.
The comical situation in the Nice defence got even worse in stoppage time as Marcin Bulka raced off his line unnecessarily, and Hamza Igamane rounded the stopper before slotting into an empty net.
Franck Haise unsurprisingly made a change during the interval, introducing Tanguy Ndombele, and again the French side started the half brightly as Gaetan Laborde forced a fingertip save from Butland.
Hicham Boudaoui then produced a stunning long-range strike but the Rangers stopper made an impressive save to preserve his side’s lead.
That stop proved pivotal as Philippe Clement’s men went four goals to the good in the 54th minute thanks to another gift in the form of a defensive mistake from Nice.
Pablo Rosario outrageously passed the ball straight into the feet of Igamane, who drove into the box and found the far corner with a tidy finish.
Four goals to the good with 30 minutes remaining, Clement took that opportunity to rest key players, making four changes.
Multiple substitutions took the sting out of the contest as a shell-shocked Nice side rarely laid a glove on Rangers after conceding the fourth.
The hosts reclaimed a moment of pride late on as Bouanani whipped home an inch-perfect free-kick, but it was nothing more than a consolation.
A stunning victory for Rangers extends their unbeaten run in visits to France to six games (W3, D3) and cements their place in the play-off positions with three games remaining, two of those against Premier League opposition in Tottenham Hotspur and Manchester United.
Nice worryingly drop to second-bottom with zero wins and just two points to their name after five Europa League games, with qualification looking unlikely.
Flashscore Man of the Match: Hamza Igamane (Rangers)