Things started disappointingly for last season's League One champions, with manager Gus Poyet sent to the stands after kicking over a crate of water bottles in the first-half and Billy Sharp handing Rovers the lead from close-range after 39 minutes.
But Buckley, a £1million summer signing from Watford, altered things with a game-changing effort from the bench, equalising in the 83rd minute and stroking home the winner deep in injury-time.
Eight minutes had been added for a nasty injury to Sharp and Buckley took full advantage with a dramatic winner.
Doncaster's first chance came in just the second minute when Sharp struck from 20 yards. Casper Ankergen got down well to save with his feet but Rovers continued to pour forward as Tommy Spurr sent a half-volley over the crossbar.
Craig Mackail-Smith earned a promising free-kick for Brighton but Kazenga LuaLua's effort was pawed over by Gary Woods.
Doncaster almost went ahead in the 19th minute when James Coppinger's whipped cross found Sharp, who trapped the ball before curling wide of the post from 12 yards.
LuaLua was cautioned for diving as Brighton struggled to impose themselves on the game and Poyet's petulant reaction saw him sent to the stands.
Ashley Barnes had a glorious chance to open the scoring against the run of play when Lewis Dunk's header caught the away defence off guard, but he delayed his shot and allowed Woods to smother.
Rovers went ahead two minutes later when Gary Dicker was dispossessed in midfield by Ryan Mason, who surged forward and found Sharp. Unlike Barnes' earlier effort, Sharp's connection was just good enough to send it trickling over the line via Ankergen.
Less than 10 minutes had passed after the restart when a poor tackle from Dunk left Sharp in some distress before being stretchered off the field.
Richard Naylor did well to clear the danger after an error from Woods and substitute Craig Noone missed a glorious chance as Doncaster allowed a rejuventated Brighton to set the pace.
Doncaster weathered that stormy period and survived again 10 minutes from time when £3.25million signing Mackail-Smith was denied again by Woods.
Buckley was given 15 minutes to change things for the home side and he was quick to get on the ball against some tired Doncaster defenders.
With eight minutes to go he levelled matters, getting on the end of Liam Bridcutt's free-kick and unleashing a sweetly-struck low shot that fizzed past Woods and into the corner.
With seconds remaining Noone and Buckley combined for the dramatic winner, the latter setting himself before burying his shot from 12 yards.