Byrne clocked 1:26.096, over half a second ahead of fellow Kawasaki rider Karl Harris.
Alex Lowes, who went fastest in free practice 2, was unhurt after crashing.
Byrne leads the shootout standings by nine points from Josh Brookes, with Lowes the only other realistic title challenger.
Third practice session times
1. Shane BYRNE 1:26.096 Kawasaki - Rapid Solicitors Kawasaki
2. Karl HARRIS 1:26.655 Kawasaki - Quattro Plant Kawasaki Superbike Team
3. Josh BROOKES 1:26.685 Suzuki - Tyco Suzuki
4. Alex LOWES 1:26.810 Honda - Team WFR
5. Michael LAVERTY 1:26.811 Honda - Samsung Honda
6. James WESTMORELAND 1:26.984 Honda - Team WFR
7. Chris WALKER 1:27.188 Kawasaki - Pr1mo Bournemouth Kawasaki Racing
8. Tommy HILL 1:27.239 Yamaha - Swan Yamaha
9. Peter HICKMAN 1:27.244 BMW - Buildbase BMW Motorrad
10. Barry BURRELL 1:27.282 BMW - Buildbase BMW Motorrad
British Eurosport is the Home of Bikes, showing all MotoGP, World Superbike and British Superbike races on Sky channels 410 and 411 and Virgin Media channels 521 and 525 as well as eurosportplayer.co.uk