Aberdeen collected three points courtesy of a Craig Ireland own goal and a counter from skipper Russell Anderson.
But Jimmy Calderwood's side had to withstand late pressure from Falkirk to hold on to the points.
Falkirk were keen to build on the previous weekend's win at Easter Road, and within the opening minute Stephen O'Donnell tested Ryan Esson with a 25-yard shot which the goalkeeper dealt with comfortably.
Alan Gow won himself a free-kick early on, and his left-foot effort breached the defensive wall but again Esson was expertly positioned to save.
The striker tried his luck again from the edge of the area shortly afterwards but hoisted his shot narrowly over.
Darryl Duffy was next to try his luck with a slightly ambitious 30-yard shot after wrestling clear of Russell Anderson, but the ball bounced harmlessly wide.
But it was Aberdeen who went in front a minute from the break. Jamie Smith played the ball in to Chris Clark, who was given too much time and space and his shot struck Ireland to leave Matt Glennon helpless.
It was the break Aberdeen needed. Within seven minutes of the second half, Anderson had added a second. The Aberdeen skipper was left unmarked as Barry Nicholson swept over a cross and, although Glennon made a fine save to keep out the initial header, Anderson followed up to bundle the ball home.
Aberdeen possessed the greater cutting edge and should have added to their lead. Steve Crawford was only inches away on a couple of occasions with shots from outside the area, and Smith completely missed a header in front of goal.
Falkirk tried to salvage things, but too often their forwards wanting too much time to tee up their shots and it enabled Aberdeen to thwart them time and time again.
Substitute Daniel McBreen made it an uncomfortable final few minutes for Aberdeen when he rammed the ball home from 16 yards. But the home side could not repeat their heroics of the previous week.