Niklas Backstrom had 35 saves for the Wild before stopping Simon Gagne and Jeff Carter in the shootout.
Philadelphia's Ray Emery stopped 10 of 11 shots before being replaced by Johan Backlund late in the second period. He saved 10 of 13.
After Sheppard put the Wild ahead 4-3 on a shot that bounced off Philadelphia's Ryan Parent into the net at 15:20, Briere pulled the Flyers even by scoring from in close at 16:56.
Koivu, who had two assists, and linemate Andrew Brunette made their first appearancers of the preseason after being sidelined with leg injuries. Minnesota right winger Petr Sykora returned after missing three games with an ankle injury.
The Flyers open the regular season at Carolina on Friday. Minnesota opens at Columbus on Saturday.