Cheltenham made a good start to the game but almost came unstuck in the fourth minute when Harry Pell's backpass was far too short, putting the league's top scorer Moses Emmanuel clear through on goal. However the stiker was denied by a fine save from Dillon Phillips, making himself large enough to snuff out the shot.
The Robins thought they should have had a penalty when Kyle Storer pulled back to Amari Morgan-Smith and the striker appeared to be brought down inside the six yard box. The referee didn't agree with teh visitor's protests and the ball was cleared to safety.
Gary Johnson's side again had Phillips to thank in the 12th minute when he got down bravely at the feet of Pierre Josheph-Dubois when the forward was through on goal.
Bromley continued to have the better of play and could have scored twice in two mintues when first Joseph-Dubois' shot came back off the post, and then Emmanuel's volley from six yards skewd wide after he had be left unmarked at the back post.
After that period of prolonged pressure from Bromley, the Robins started to hold onto the ball better and create a few chances of their own. Pell and Morgan-Smith both shooting just wide from distance after good hold up play from Danny Wright.
Jack Munns thought he had given his side the lead, only for his shot from close range to be deflected wide, Aaron Downes then met the resulting corner with a powerful header, only to be denied by a fine reaction save from Chris Kettings in the Bromley goal.
Both sides got into good positions to score before the break but lacked the final ball, so the first half ended goalless.
Cheltenham came out the stronger side and almost scored straight away, but Munns' 20 yard effort didn't cross the line after smashing off the underside of the bar.
The Bromley fans thought Emmanuel had scored soon after when his curling effort looked destined to fire into the top corner, only for Dillon Phillips to produce another incredible save, throwing himself full length to his left to push the ball away.
Both managers made subs to try and find a winner around the hour mark, with Gary Johnson bringing on Billy Waters to replace Morgan-Smith in the 65th minute.
Neither side we able to create many chances in the second half, with both defenses on top, in particular Daniel Parslow and Sean Francis.
The deadlock was finally broken in the 78th minute when super-sub was fastest to react when Bromley keeper Kettings could only parry a long range Kyle Storer effort. The striker had time to control the ball and slot it home to give the Robins a 1-0 lead.
Gary Johnson brought on Asa Hall and Lee Vaughan for Harry Pell and Jack Barthram respectively to try and sure up the scoreline.
Just when it looked like Cheltenham were going to see it out easily George McLennan rashly brought down Anthony Cook inside the box to concede the penalty in the 88th minute. Cook dusted himself down to smash the penalty home and seemingly earn himself the point.
However, as always with the Robins, there was more drama to come in injury time. The ball dropped to Asa Hall 10 yards out and the midfielder thundered the ball home to send the travelling fans, directors and players wild!
Bromley had little time to respond and the match ended 2-1 to the Robins!
Emmanuel Udoji, Ben Chorley, Rob Swaine (c), Joe Anderson
Pierre Joseph- Dubois, Ali Fuseni, Reece Prestedge, Anthony Cook
Moses Emmanuel, Jack Holland
Rob Dickie, Aaron Downes (c), Daniel Parslow
Jack Barthram, Harry Pell, Kyle Storer, Jack Munns, George McLennan
Amari Morgan-Smith (65, Billy Waters), Danny Wright