Kurtis Guthrie's first-half brace put the visitors in control, his first coming from a redirected Brett Williams' shot before a close-range second just before half-time.
Pierre Joseph-Dubois halved Bromley's deficit from six yards out.
Despite Paul Rogers sending' off, Holland rescued a point for Bromley when he headed home in stoppage time.
Forest Green boss Ady Pennock told BBC Radio Gloucestershire:
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"I'm very annoyed. They let me down today, they let all my staff down. To go 2-0 up, 10 men, the second half is just not acceptable.
"Why should I be on the sidelines shouting and hollering, it all comes to how badly they really want it, I badly want it, all my staff badly want it, the fans want it.
"It all depends if they really want it and some of them have really got to look at themselves now because Cheltenham are in the hot seat."
Jack Holland scored an injury-time equaliser for Bromley to dent Forest Green Rovers' automatic promotion bid.