The versatile Cooper, who had made 78 appearances for the Canberra-based Brumbies before moving to Sydney in 2012, scored in the 46th minute of the match which was a stop-start affair with neither side able to develop any continuity.
Both teams were also heavily penalised, particularly at the breakdown, by referee Steve Walsh, which lead to Waratahs scrumhalf Brendan McKibbin slotting six penalties, while Force flyhalf Sias Ebersohn kicked four.
"It was tough, we made it hard on ourselves," Waratahs captain Dave Dennis said in a pitchside interview. "We didn't perform how we wanted to in some areas."
"There wasn't a lot between us ... but we have got the points and it worked out well."
The Force actually started with purpose, stringing phases together and driving down the field to go out to a 6-0 lead courtesy of two penalties from Ebersohn.
The Waratahs, however, slowly built back into the game with McKibbin slotting two penalties as the home side began to throw the ball wider and build phases themselves.
Force prop Salesi Ma'afu was then sin-binned for a high tackle on Waratahs hooker Tatafu Polota-Nau about 20 minutes into the first half, which allowed McKibbin to slot three more penalties.
Ebersohn managed to reduce the gap just before the break to go into half-time trailing 15-9.
McKibbin slotted his fourth penalty of the game just a minute after the restart before Ashley-Cooper finished off a break from Israel Folau to give the home side a seemingly-comfortable 23-9 lead.
Force fullback Alfie Mafi, however, dragged his side back into the game when the Perth-based side managed to string more than three phases together and Ebersohn converted and added his fourth penalty to make the last 20 minutes close.
Waratahs prop Benn Robinson, who was also celebrating his 100th Super Rugby game, however fittingly provided the coup de grace when he snaffled the ball at a turnover after the full-time hooter sounded and the Waratahs kicked the ball into touch.
Scorers:Waratahs:
Try: Adam Ashley-Cooper
Penelaties: Brendan McKibbin (6)
Force:
Try: Alifeleti Mafi
Conversion: Sias Ebersohn
Penalties: Ebersohn (4)
Teams:
Waratahs:
15 Israel Folau, 14 Peter Betham, 13 Adam Ashley-Cooper, 12 Rob Horne, 11 Drew Mitchell, 10 Bernard Foley, 9 Brendan McKibbin, 8 Pat McCutcheon, 7 Michael Hooper, 6 Dave Dennis (captain), 5 Kane Douglas, 4 Sitaleki Timani, 3 Paddy Ryan, 2 John Ulugia, 1 Benn Robinson
Substitutes: 16 Tatafu Polota-Nau, 17 Sekope Kepu, 18 Mitchell Chapman, 19 Jed Holloway, 20 Matt Lucas, 21 Ben Volavola, 22 Tom Kingston
Force:
15. Alifeleti (Alfi) Mafi, 14. Patrick Dellit, 13. Winston Stanley, 12. Kyle Godwin, 11. Junior Rasolea, 10. Sias Ebersohn, 9. Alby Mathewson, 8. Richard Brown, 7. Matthew Hodgson (captain), 6. Ben McCalman, 5. Hugh McMeniman, 4. Toby Lynn, 3. Salesi Ma'afu, 2. Heath Tessmann, 1. Pekahou Cowan
Substitutes: 16. Ben Whittaker, 17. Kieran Longbottom, 18. Sam Wykes, 19. Chris Alcock, 20. Chris Eaton, 21. Sam Christie, 22. Sam Norton-Knight