The pair struck in the final 20 minutes after Pirates conceded either side of the break of the first leg tie in Libreville, Gabon.
Bucs, who also relied on a strong display from goalkeeper Brighton Mhlongo, will host the return duel in a fortnight as they seek to advance to the group stages of the CAF showpiece.
The hosts scored in the 30th minute and on the hour-mark, with the second coming from the spot after defender Ayanda Gcaba was adjudged to have fouled in the box.
However, Majoro, a half-time replacement for rare starter Thamsanga Gabuza, drew level in the 70th minute before the tricky Rakhale fired into the net shortly after coming on.
Eric Tinkler's charges beat Uganda Revenue Authority 4-3 on aggregate in the previous round of the tournament.
The Sea Robbers are the only team from South Africa still playing on the continent after both Kaizer Chiefs and Mamelodi Sundowns were booted out of the Champions League in the first round.