The Stormers produced a vastly improved attacking display but it was not enough to earn them a highly sought-after bonus point.
Leading 16-6 at the break, a bonus-point seemed possible after the Stormers scored two first-half tries.
In the second half, however, the Stormers showed a fair amount of enterprise but could not add to their first-half try count.
In the opening minutes, there was a succession of kicks from both sides and a reluctance to run the ball from anywhere within their own half.
The ploy did not bring any reward as the kicks were always too deep and did not pose problems inside the opposition half.
The Waratahs resorted to Berrick Barnes repeatedly kicking up-and-unders but the Stormers' backs, notably Joe Pietersen (fullback), Gio Aplon (wing) and Peter Grant (flyhalf), showed great courage with number of brave catches under pressure.
On one occasion, the Stormers failed to clear adequately as they infringed and scrumhalf Brendan McKibbin goaled the resultant penalty (3-0).
The Stormers, on the other hand, changed gear after 10 minutes and showed enterprise by opting for strong runs with ball in hand.
Aplon provided the spark with a fine break from the halfway line before he was held up 10 metres out.
The Stormers spun the ball wide from the breakdown and Pietersen dived over the corner for the opening try of the match. Grant's conversion failed (5-3).
Pietersen made it 8-3 in the 22nd minute with a 35-metre penalty and this advance gave the Stormers' game a decided lift before the halftime break.
The Waratahs were forced to settle for a defensive role and they did well to stifle several promising sorties into their 22-metre area, except one which materialised in a try by hooker Tiaan Liebenberg.
The conversion by Grant failed but he atoned with a penalty a few minutes ahead of the break (16-3).
The Waratahs took the Stormers by surprise at the start of the second half with a strong attack down the outside far right channel where centre Rob Horne rounded off splendidly with a try (16-8).
McKibbin followed his conversion with a penalty moments later and reduced the deficit to three points (16-13).
The Stormers shrugged off the setback with a penetrative move past the Waratahs 10-metre line and their pressure caused the visitors to incur a penalty which Grant goaled to open up a six-point lead (19-13).
Every so often, the Stormers opened up the game with some fine attacking play but the Waratahs' defence coped well with all the variations thrown at them.
Tries - J. Pietersen, T. Liebenberg
Pen - J. Pietersen, P. Grant 2
Tries - R. Horne
Pen - B. McKibbin 2
Con - B. McKibbin
Referee: Craig Joubert
Assistant Ref 1: Stuart Berry
Assistant Ref 2: Christie Du Preez
TMO: Shaun Veldsman
15. Joe Pietersen, 14. Gio Aplon, 13. Juan de Jongh, 12. Jean de Villiers (captain), 11. Bryan Habana, 10. Peter Grant, 9. Dewaldt Duvenage, 8. Jebb Sinclair, 7. Rynhardt Elstadt, 6. Siya Kolisi, 5. Andries Bekker, 4. Eben Etzebeth, 3. Brok Harris, 2. Tiaan Liebenberg, 1. Steven Kitshoff
Substitutes: 16. Deon Fourie, 17. Frans Malherbe, 18. De Kock Steenkamp, 19. Don Armand, 20. Louis Schreuder, 21. Burton Francis, 22. Gerhard van den Heever
15. Bernard Foley, 14. Atieli Pakalani, 13. Rob Horne, 12. Adam Ashley-Cooper, 11. Tom Kingston, 10. Berrick Barnes, 9. Brendan McKibbin, 8. Dave Dennis, 7. Chris Alcock, 6. Rocky Elsom (c), 5. Sitaleki Timani, 4. Dean Mumm, 3. Sekope Kepu, 2. John Ulugia/Tatafu Polota-Nau, 1. Benn Robinson.
Res: 16. Josh Mann-Rea, 17. Jeremy Tilse, 18. Kane Douglas, 19. Jono Jenkins, 20. Wycliff Palu, 21. Sarel Pretorius, 22. Daniel Halangahu