The pair scored late in the game to put Monaco on 68 points from 39 matches, ahead of second-placed Nice, as they geared up for Wednesday's Champions League last-16 return leg against Manchester City after a 5-3 defeat in the away leg.
Bordeaux responded with an 84th minute goal by Diego Rolan but Monaco held firm.
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Nice have 63 points after salvaging a 2-2 draw at home to Caen on Friday, while Paris St Germain, who travel to Lorient on Sunday, are a further point back in third spot.
Monaco wasted several chances in the first half before hitting their stride when striker Radamel Falcao came off the bench in the 64th. Four minutes later, Mbappe tapped the ball in from the Colombian's pass.
Moutinho scored with a delightful first-time curling shot into top left corner in the 74th after Bernardo Silva found his fellow Portuguese with a 25-metre cross.
Bordeaux reduced the arrears when Rolan intercepted a pass back to Danijel Subasic, who waited too long to clear the ball.
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