McSweeney's horse, Barrow Island, ridden by Johnny Murtagh and trained by Michael Halford, won the Leopardstown Cup by a length-and-a-half from Francis Brennan's Six Silver Lane.
The remaining horses, Colour of Love (Jean Byrne), Crystal Morning (Alan Quinlan) and Toufan Express (Mike Denver), crossed the line in a tight finish.
Linda Martin watched from the grandstand having been eliminated in a race-off at the Curragh the previous week.
Commenting on her win, McSweeney said: "I'm absolutely over the moon! It's just amazing. It's about more than just this win, it's about everyone who's been involved in the team.
"The star of the show for me has been Michael Halford. To get a grasp of the decisions he has to make and how he makes them has been brilliant. It's a whole world that has opened up for me now."
Trainer Halford said: "It's wonderful for the whole team. It's a tribute to them that this horse has won today - the condition he's in and the great help from Ella and her great advice."
Ray McCarthy, RTÉ Commissioning Editor for Regional Programmes, added: "Stars Go Racing delivered great entertainment this summer and gave our viewers a real insight into the world of horse racing. We were delighted to work with Horse Racing Ireland and are really pleased that Stars Go Racing has been such a big success."