Wanderers had taken a first-half lead after Seagulls winger David Lopez put through his own net, but four second-half minutes saw Brighton score three times to leave Dougie Freedman's men still without a win this season.
Jay Spearing put through his own goal in the 53rd minute, before Inigo Calderon and Will Buckley both found the net to stretch the Amex club's unbeaten run to six matches.
David Ngog failed to keep his cool when one-on-one with keeper Tomasz Kuszczak, who made a save down low to deny the French striker after a mix-up in the Brighton defence.
Darren Pratley's first-half header from Marc Tierney's cross had given Wanderers the lead.
But David Wheater then gave away a penalty in the early stages of the second half to give Blackman the chance to equalise, which he duly converted to earn the Royals a point.
Freedman said: "I felt that it was a good match and we were outstanding in the first 45 minutes.
"But fair play to Reading. They looked like a Premier League side today and they counter-attacked us really well.
"I will be amazed if they aren't in the top six. We've played a really top team there and there wasn't much in it.
Reading manager Nigel Adkins, meanwhile, defended the referee's performance despite two further penalty decisions not going their way.