The Team of Choice hit the woodwork, had a couple of penalty appeals turned down and also saw home keeper Boy de Jong making a succession of big saves.
The first half was fairly evenly balanced, both sides having chances, the first of those falling to Thabiso Kutumela – whose angled drive went marginally wide in the seventh minute.
With 27 minutes gone, Kutumela curled a shot wide after an incisive break.
Towards the end of the first half, Maritzburg keeper Richard Ofori was given work to do and he came out trumps as he tipped over an Iqraam Rayners flick from close range, before saving headers from Alan Robertson and Morgan Gould.
The Team of Choice came out firing after the restart and were unlucky not to go take the lead when following a goal box scramble, Daylon Claasen struck the post.
United kept the pressure on as Kutumela shot wide, before the Maritzburg striker was played in on goal by Mohau Mokate but was then denied at close range by home keeper Boy de Jong – who made a last-gasp block with his legs.
As the match moved into the final 10 minutes, the Team of Choice upped the ante even further. But de Jong continued to keep them at bay as he blocked a Rushine de Reuck header from point-blank range, the ball striking the goalkeeper on the head and bouncing clear.
Maritzburg also came close with a succession of late corners, as well as having an appeal for a handball ignored.
The KZN Midlands side are next in action against Black Leopards at the Harry Gwala Stadium on Wednesday night.
Stellenbosch: 31. De Jong, 20. Robertson, 5. Mthethwa, 47. Gould, 13. Van Heerden, 15. Bergman, 6. Moroole, 8. Matsi, 11. Franco, 10. Rayners, 29. Moon.
Subs: 35. Langeveldt, 3. Ndlovu, 4. De Goede, 9. Du Preez, 18. Skelem, 21. Isaacs, 50. Zungu.
Maritzburg: 31. Ofori, 25. Xulu, 4. Allie, 5. Morgan, 23. De Reuck, 45. Mngonyama, 6. Timm, 17. Claasen, 7. Kutumela, 22. Mokate, 28. Mekoa.
Subs: 30. Mpandle, 15. Ntshangase, 26. Shandu, 8. Buchanan, 20. Moseamedi, 13. Lea'Alafa, 36. Kunene.