Jabulani Maluleke, who also missed a penalty in the dying minutes, opened the scoring for Leopards, while Gareth Ncaca equalised for United.
However, had Maluleke scored from the spot, it would have made no difference to the outcome, as Leopards would still have lost on the away goal rule.
Leopards, who went into this game trailing by 1-0 from the first leg, were by far the better team for most of the match and deservedly went ahead in the 17th minute when Maluleke headed home from close range following a cross by Mulondo Sikhwivhilu.
The hosts thought they had doubled their lead in the 29th minute when Myron Shongwe slid home a cross by Sikhwivhilu, but the striker’s effort was ruled out for offside.
Gareth Ncaca leveled matters for Bay United in the 38th when slotted home a superb free-kick from the edge of the area.
The score remained 1-1 at half-time, and Leopards continued their impressive play in the second half.
However, they found United keeper Arthur Bartman in superb form, as he produced numerous saves to deny the hosts.
Abayomi Adebayo should have sealed the match for the visitors in the 61st minute when he found himself clear on goal, facing an empty net, but the striker somehow managed to send his first time shot, from inside the area, wide of goal.
The one time that Leopards managed to beat Bartman, they were denied by the woodwork, as Maluleke saw his free-kick come back off the crossbar in the 63rd minute.
Leopards were awarded a penalty two minutes into referee Jerome Damon’s optional time, but again Bartman rose to the occasion, as he denied Maluleke from the spot.
Bay United will now meet FC AK, who beat Dynamos, in the promotion play-off final, which will be played over two legs, with the first leg set for Wednesday, July 9 and the second will be played next Sunday, July13.