Monaco's Radamel Falcao (R) celebrates after scoring a goal against Dijon on April 15, 2017 at the Louis II Stadium in MonacoMonaco's Radamel Falcao (R) celebrates after scoring a goal against Dijon on April 15, 2017 at the Louis II Stadium in Monaco (AFP Photo/VALERY HACHE)
Cedric Varrault's goal had struggling Dijon in front at the Stade Louis II but Nabil Dirar poked in following a Falcao free-kick to equalise on 69 minutes and the Colombian netted from another dead ball to secure the points.
Monaco's sixth straight league win allows them to once again move three points clear at the top from defending champions Paris Saint-Germain, who won 2-0 at Angers on Friday thanks to an Angel Di Maria brace.
Nice are a further point adrift in third after coming from behind to beat Nancy 3-1 earlier on Saturday, although they have played a game more.
Monaco coach Leonardo Jardim made four changes to his team from Wednesday's 3-2 Champions League quarter-final first-leg win away to Borussia Dortmund.
Falcao was one of those who made way and Dirar one of those to come into the line-up for a potentially awkward fixture in between the two legs against Dortmund.
Last midweek's first leg was postponed by 24 hours following the bomb attack on the German team's bus and the return will be next Wednesday at the Stade Louis II.
Monaco have insisted winning the French title is their primary objective but they found themselves behind at half-time against relegation threatened opponents.
Danijel Subasic saved from a Julio Tavares header but Varrault, a 37-year-old defender, was on hand to score the rebound.
Falcao was introduced with half an hour left and the former Atletico Madrid man was the catalyst for the comeback that allowed Monaco to stay on track for a first title since 2000.
He made the equaliser when his free-kick struck the underside of the bar and hit the backside of Dijon goalkeeper Baptiste Reynet, allowing Dirar to poke home.
And the hosts won it with nine minutes to go when Falcao curled in another free-kick for his 18th league goal of the season as Monaco extended their unbeaten run to 14 league matches.
- Nice into Champions League -
Pocket-sized midfielder Jean Michael Seri netted twice in the second half as Nice came from behind to beat Nancy and secure a crack at next season's Champions League.
Junior Dale gave struggling Nancy the lead at the Allianz Riviera after Nice failed to clear their lines at a corner.
But for the fifth straight game they fought back from behind, and this time they did so without 13-goal top scorer Mario Balotelli, who was suspended.
Younes Belhanda set up Mickael Le Bihan to equalise 10 minutes before the interval as the striker marked his first start since September 2015 with a goal.
Seri put the home side ahead six minutes after the break from the penalty spot after Dalbert had been fouled by Issiar Dia and the Ivorian struck again late on to secure the victory.
While they remain in with a chance in the title race, the win also means Lucien Favre's side are guaranteed a top-three finish and so they will represent France in the Champions League for the first time next season.
"We all had a little beer to celebrate the victory. Who doesn't want to play in the Champions League?," said Swiss coach Favre as Nice made sure of their highest finish since 1976.
"I was 19 when I started playing against Nice in 1976 in the Cup of the Alps. They were a great side. As for us, we are having a superb season but we need stability over several seasons and to keep progressing."
There were also wins on Saturday for Guingamp, Lille and Montpellier, with the latter beating Lorient 2-0 to leave the Brittany side still in the bottom three.