Tuks were especially nervy in sitting on their lead and conceded a penalty which allowed Letsoalo to get his team on the board.
Letsoalo was on hand to convert when Tuks failed to deal with a ball into their area and levelled matters in the 79th minute of the cup match.
It looked like extra time would be required to separate the sides however Royal AM showed desire late in the piece.
Coach John Maduka brought on the attacking cavalry though. Tebogo Potsane came on for Macuphu, Menzi Masuku replaced Mashikinya, and Jabulani Ncobeni also took over from Ricardo Nascimento.
Royal AM had other ideas though. They moved the ball forward in a lightning-quick attack that ended with Mfundo Thikazi burying a tap-in following a superb square ball from Sedwyn George.
Watch: Royal AM snatch Nedbank Cup tie
Nedbank Cup: Royal AM 3-2 University of Pretoria
Royal AM: 16. Nyame, 20. Mkhize, 14. Matlaba, 24. Lingwati, 3. Nascimento, 18. Mashikinya, 12. Mahlasela, 10. Mabena, 6. Kobedi, 9. Macuphu, 21. Letsoalo.
Subs: 1. Heugh, 11. Potsane, 22. Rikhotso, 34. Thikazi, 42. Ncobeni, 50. Masuku, 45. George, 19. Matjila, 7. Pelembe.
University of Pretoria: 25. Msibi, 4. Allan, 33. Maqoko, 42. Moeketsi, 19. Mpedi, 23. Julies, 20. Mvambi, 30. Barns, 3. Chokoe, 34. Makhubu, 28 Pheeane.
Subs: 26. Cola, 16. Phewa, 12. T. Mokoena, 29. Selotola, 32. Msani, 15. B.Mokwena, 36. Sibanyoni.