Falkirk boss John McGlynn emphasised the need to use his squad amid a hectic programme, with Calvin Miller and Brad Spencer among those carrying knocks and given finishers' roles.
McGlynn had made five changes for Sunday's Scottish Cup win over League One Stenhousemuir, and made one more for his team's return to Premiership duty.
While Dundee edged the midfield battle and had their moments down the left flank, Hogarth had very little to do, with his defenders contributing vital blocks when shooting opportunities arose.
Where Dundee were toothless or wasteful, Broggio was clinical. The teenager's neat finish - one touch to cushion on the knee, another to stroke home - proved decisive, and enhanced his growing reputation among the Falkirk fanbase.
Dundee are the lowest scorers in the Scottish Premiership, with a measly 19 goals from 25 matches. This was the 13th time they have failed to score in a league game this season.
Pressley can be encouraged by his team's ability to build attacking phases, using the pace and trickery of Tony Yogane down the left or the bustling forays of Graham from the back and through the middle.
What they lacked, yet again, was a killer touch. In fact, for all their fluency and all their endeavour, Hogarth was seldom troubled until he chopped down Bevan at the death.
Dhanda - whose goal, from the spot, settled this fixture in December - fluffed his lines. A fitting summation of Dundee's predicament.