Mbappe and Moutinho keep Monaco in the lead
Mbappe opened the scoring midway through the second half at the Stade Louis II and a beauty from Joao Moutinho soon after doubled the principality side's lead.
They held on to take all three points after a howler from goalkeeper Danijel Subasic allowed Diego Rolan in to reduce the arrears.
Monaco, who will look to overturn a 5-3 first-leg deficit when they host Manchester City in their Champions League last-16 return on Wednesday, are five points clear of local rivals Nice at the top of the table with nine games left.
However, Paris Saint-Germain can go back up to second and cut Monaco's lead back to three points with a win at bottom club Lorient on Sunday in their first outing since their Champions League humiliation in Barcelona.
Nice lost ground on Friday despite coming back from two goals down to draw 2-2 at home to Caen, Mario Balotelli and Anastasios Donis getting their goals.
Monaco are looking to win the French title for the first time since 2000. They had not beaten Bordeaux at home since 2003 and that run looked set to continue as the usually irresistible Monaco attack struggled to fire.
Moutinho was recalled in place of Tiemoue Bakayoko in the home midfield while Mbappe again partnered Valere Germain up front with Radamel Falcao on the bench.
That decision was surely made with one eye on the clash with City, but Leonardo Jardim's side were still looking for the opening goal when the Colombian striker was introduced in the 64th minute.
Cedric Carrasso boxed away a powerful Thomas Lemar strike in the first half and Mbappe had a header cleared off the line by Milan Gajic as Bordeaux frustrated their hosts.
Bordeaux needed points as they chase European qualification but they fell behind after some questionable defending in the 68th minute.
Falcao got his head to a left-wing corner, neither Gaetan Laborde nor Yonousse Sankhare cleared, and Mbappe side-footed home.
It was a 16th goal in all competitions this season for the 18-year-old, who has developed into one of the hottest prospects in European football.
Portugal playmaker Moutinho made it 2-0 in the 74th minute, running onto a Bernardo Silva pass and floating a stunning shot high into the far corner.
But like in their Champions League thriller with City, Monaco showed signs of defensive weakness as they gave Bordeaux hope late on.
Subasic came out of his area in an attempt to clear, but the ball struck off the advancing Rolan, ricoheted back off the Croatian goalkeeper's face and the Bordeaux player ran in to finish into an empty net.