Conor McGrandles and Rory Loy scored the goals but the home side could have won by a greater margin. Phil Roberts passed up two or three decent opportunities and Loy saw a penalty saved late in the first half.
This was another impressive display from a young team growing in confidence who have now managed six successive clean sheets.
Dundee gave a debut to new signing Christian Nade but he was withdrawn after less than 45 minutes.
By that stage, Falkirk led through McGrandles, who had time to control a Roberts cross before scoring at the near post and Loy had been brought down by Kyle Letheren as he was set to apply his finish.
The red card inevitably followed for the Dundee goalkeeper and Nade was sacrificed to allow replacement goalkeeper Dan Twardzik to come on.
His first action was to save an admittedly weak Loy penalty as the first half came to a close but Falkirk killed it off after the break.
Roberts provided the cross for Loy to make amends for his penalty miss and score the clinching goal from close range.
In a memorable match at New Douglas Park, Cowdenbeath held off a late fightback from Hamilton Academical to win 4-3 and deny their opponents the chance to go top.
Cowdenbeath were 4-0 up shortly after half-time but Hamilton almost salvaged a point in a stirring finish. New signing Jason Scotland made his debut for Hamilton up front but it was Cowdenbeath who caught the eye with their attacking play.
Greg Stewart scored with a low shot from 10 yards after just five minutes and, before Hamilton had time to recover, Kane Hemmings added a second, guiding the ball home from just outside the area.
Hemmings stunned the New Douglas Park crowd when he added his second and Cowdenbeath's third after he controlled a superb pass from Lewis Milne and rifled the ball past Kevin Cuthbert.
Worse was to follow for Hamilton after half-time and Stewart side-footed his second goal after Hemmings had galloped clear and laid the ball back.
But Hamilton pulled a goal back through Tony Andreu and, with Hemmings and Stewart having been substituted, attempted to salvage the game. James Keatings scored a second goal from the penalty spot after Scotland had been fouled in the area.
Hamilton pressed for a third goal to make the final stages uncomfortable for Cowdenbeath and it duly came when Andreu's free-kick took a wicked deflection to make it 4-3 but Hamilton could not find the equaliser.
Morton's match with Queen of the South was abandoned after just 10 minutes after a spectator in the main stand collapsed and died.
Referee Don Robertson immediately halted the game as the gravity of the situation became obvious.
Ambulance crew moved in to give emergency treatment to the spectator but they were unable to save him.