Jay Rodriguez's 15th goal of the season put Burnley ahead but Bellamy struck at the end to ensure the Bluebirds finished level on points with the Swans.
Yet Swansea thrashed relegated Sheffield United at the Liberty Stadium and their superior goal difference meant Dave Jones' men - beaten in last season's Championship play-off final - now face in-form Reading over two legs in the play-off semi-finals.
Rodriguez's strike marked another feather in his cap after he was this week included in the provisional England squad for the European Under-21 Championship finals in June.
The Burnley-born frontman opened the scoring in the 13th minute with a fine right-footed strike into the bottom left-hand corner from 18 yards.
But, in the last minute, Stephen McPhail found Bellamy and he fired a low left-footed shot into the net from 18 yards.
Source: PA
Source: PA