However, the Seagulls still slipped off the top of the Championship table while Town avoided tumbling to the bottom on Tuesday night.
Daryl Murphy fired the lowly Tractor Boys into the lead in the first half, but they were denied a first win in eight games, and some breathing space for under-pressure boss Paul Jewell, when Buckley struck from close range with 10 minutes to go.
Brighton could have gone ahead after just 30 seconds when some neat play from Ashley Barnes and Stephen Dobbie teed up Kazenga LuaLua but the former Newcastle winger scuffed his shot wide.
Barnes then played in Dobbie, still looking for his first goal since joining from Swansea, but his low shot was saved by Scott Loach.
Ipswich were looking dangerous as well, though, and Tomasz Kuszczak kept out a drive from Jay Emmanuel-Thomas before Murphy headed a Carlos Edwards cross wide.
And in the 27th minute, it was the visitors who took a shock lead when another deep Edwards deep cross to the far post again found Murphy, who this time stooped to plant his header past Kuszczak.
Brighton almost pulled one back before the interval but Wayne Bridge's shot was deflected narrowly wide.
Yet just after the break Ipswich were agonisingly close to doubling their advantage, again through Murphy.
Michael Chopra's cross fizzed across the Brighton goal and Murphy's shot was kept out by the legs of the diving Kuszczak.
But the Seagulls bossed the majority of the second half and Dobbie's deflected shot looped over, LuaLua was denied by Loach and a smart turn and shot from Barnes flew inches wide.
Boss Gus Poyet threw on Buckley and Gary Dicker just after the hour mark, and the substitution paid dividends 18 minutes later.
They finally drew level after Inigo Calderon's persistence down the right was rewarded when his cross-shot ricocheted to Buckley, who was in the right place to tap the ball in from a yard out.
Ipswich had a chance to go back into the lead moments later when Jason Scotland curled the ball towards goal and although Kuszczak fumbled the shot, Brighton cleared the danger.
Brighton went for the win during five minutes of stoppage time, with Buckley the driving force, but his curling cross was just too far in front of Barnes as the hosts had to settle for a point.