Majoro netted on the stroke of half-time in Phokeng for his eighth League goal, and 11th in all competitions this season.
However, the ex-Kaizer Chiefs man - who struck in the 2-1 win at AmaZulu in midweek - was shown a straight red card for a blatant stamp on Mahlatsi Makhudubela just past the hour-mark.
Stars, though, were unable to exploit the numerical advantage, with Bucs substitute Lennox Bacela adding a second goal in the final minute.
The result leaves Pirates fourth on the Absa Premiership table with 32 points from 19 games - 15 points shy of leaders Kaizer Chiefs, and two behind champions Mamelodi Sundowns and Bidvest Wits.
Dikwena remain in the relegation zone with 18 points from as many matches, nine points above AmaZulu, who have a game in hand.
The visitors dictated the pace early on but struggled to fashion clear cut goal scoring chances.
Issa Sarr came close for Pirates in the 15th minute when his header at a corner-kick went narrowly wide, but chances were generally at a minimum.
Stars should have gone ahead in the 35th minute when Ndumiso Mabena broke through on goal and beat the keeper, but his goal was incorrectly disallowed for offside.
Ten minutes later Pirates finally made their pressure count when Majoro finished after being released by Man of the Match Oupa Manyisa.
Stars were the better side in the second half, but again passing in the final third was poor and chances on goal were hard to come by.
In the 62nd minute the game sprang into life when Pirates were reduced to ten men after Majoro was dismissed for a stamp on Makhudubela.
Dikwena pressed forward after that and came closest to equalising in the 85th minute when Eleazar Rodgers struck the crossbar with a bicycle kick from 10 yards.
Five minutes later Bacela guaranteed Pirates the win when he slotted into an empty net following a mistake by goalkeeper Kabelo Dambe.