Buckley struck in either half as Albion continued their fine run in form, having only lost once in the league in their last seven matches which has seen them move one point behind sixth-placed Nottingham Forest.
The defeat ended Wanderers' four-match unbeaten sequence and their season now looks well and truly over.
Dougie Freedman was still without Matt Mills and Jermaine Beckford, while the visitors were able to call their captain Gordon Greer back after suspension.
However, the Seagulls were unable to field midfielder Keith Andrews, who is on a season long loan from the Trotters.
Both teams had chances early on in a fast start to the match. Brighton threatened first when Leonardo Ulloa's cross almost unintentionally crept into the top-right corner before Bolton goalkeeper Adam Bogdan pushed it out for a corner.
Bolton then hit back after Chung-Yong Lee and Lukas Jutkiewicz combined in the Seagulls area, and it took a heroic block from defender Lewis Dunk to keep striker Jutkiewicz at bay.
Ulloa curled a ball into the box, which connected perfectly with Buckley's boot at pace at point blank range. Somehow Bogdan managed to parry the ball out, but Wanderers were sluggish to rebound and Buckley then quickly fired into the bottom corner while on the turn.
That forced Wanderers into being more attacking-minded. Lee had placed a shot from range which was tipped over by Thomas Kuszczak. The former Manchester United stopper was then on hand to save David Wheater's bullet header that came from the South Korean international's corner.
They came even closer to equalising just before the break. Medo Kamara's free kick from just outside the box clipped the top of the wall and hit the cross bar to the relief of Kuszczak.
The Trotters came out on the front foot again after the break and, as Brighton were defending for their lives, it looked as though they grabbed the equaliser.
In a crowded area, Lee got a shot away, which deflected off Joe Mason into the back of the net. But, despite the jubilation, the linesman had his flag up for offside.
That disallowed goal seemed to deflate the home side and five minutes later Brighton doubled their lead.
A mistake from Kamara in midfield put Buckley one-on-one with Bogdan. The former Watford winger made no mistake, getting his left-footed shot off early, which curled into the bottom left corner.
Bolton had a few half chances late on, but never really threatened to get back in the game, with Brighton claiming their eighth clean sheet from their last eight wins.