A 50-metre set-shot from Ebert with little over 10 seconds remaining saw the Power record a 14.4 (88) to 13.9 (87) victory in Ken Hinkley's first game in charge.
The Power kicked nine unanswered goals to overturn a 39-point deficit before the Bulldogs hit the front again with four goals of their own.
However, playing their first game since the death of talented youngster John McCarthy in September, the Power clinched victory with two goals in as many minutes.
New recruit Angus Monfries and Cameron Hitchcock led the way with three goals apiece, while acting captain Shaun Higgins was the Bulldogs' leading goalkicker with three goals.
Port Adelaide kicked the first goal of the game through Jasper Pittard before the Bulldogs responded with goals from big man Ayce Cordy, Alex Greenwood, Luke Dahlhaus and Patrick Veszpremi, who finished with two.
The Bulldogs held a 15-point lead heading into quarter-time and they extended that advantage to just over four goals before half-time.
Goals from Veszpremi and new recruit Koby Stevens ensured the Bulldogs maintained their ruthlessness in the third quarter but led by acting captain Hamish Hartlett, the Power closed to within a kick after falling 39 points behind at one stage.
Port Adelaide's rally continued in the final term, the Power hitting the front early on before they opened up a 14-point lead off the boot of Monfries.
The Bulldogs mounted a comeback of their own with four goals in quick succession to regain the ascendancy.
But in a seesawing tussle, Ebert converted a shot from the boundary line as the Power claimed the right to contest next year's exhibition match in London.