Monaco trailed until the 69th minute following Cedric Varrault's opener, but Nabil Dirar's equaliser and a 25-metre free kick from substitute Falcao took them up to 77 points, three clear of Paris St Germain and four ahead of Nice.
Monaco were forced to play their midweek Champions League game a day late following the attack on the Borussia Dortmund bus ahead of their quarter-final first leg, and despite picking up a valuable 3-2 win on Wednesday, they struggled to muster the same intensity against Dijon.
"It's difficult to play in the Champions League and Ligue 1," Monaco coach Leonardo Jardim told the club's official website. (www.asmonaco.com) "We need to manage our players.
"All of our matches are going to be difficult," Jardim added. "We need to win and we need all of our squad."
The visitors took the lead in the 42nd minute when Danijel Subasic stopped Julio Tavares's header on his goalline only for the quick-thinking Varrault to race in and tap home.
Dirar, however, equalised for the home side in the 69th minute when he reacted first and finished from close range after a fine Falcao free kick cannoned down off the woodwork, before the Colombian striker added a second from range nine minutes from time.
"Falcao is a goalscorer. He offers us offensive quality and efficiency," the coach said. "It was a deserved victory."
Earlier, Nice boosted their hopes of a first French title since 1959 when two second-half goals from the outstanding Jean Seri inspired them to come from behind to down Nancy.
Read the full article on eurosport.co.uk: Monaco come from behind to beat Dijon, Nice reach Champions League