Aldershot, which had been two goals behind at the time of their visit, rallied from a deficit to win 3-2.
Bromley scored twice in just four minutes during the National League match. Louis Dennis lobbed Jordi Van Stappershoef, before Michael Cheek added the second.
The Shots began their comeback when Jack Barham scored from the inside of the penalty area in the 58th-minute.
Lorent Tolaj, who had his back turned to the goal and was able to shoot into the corner of the net from the outside area in the 73rd minutes, brought the score level.
The Bromley team had Byron Webster dismissed after he clashed with Kwame Thomas mid-air. And the advantage of having a man in front paid off in stoppage time, when Rowe nodded to snare all three points.
