The Raiders will now play the Grand Final Qualifier at Craven Park against Halifax or Sheffield.
The Eagles’ win places them in second place, but Fax could reach second spot when they host Toulouse Olympique on Sunday.
That advantage was extended after the restart when Trevor Exton’s kick to the in-goal area was touched down by Danny Mills.
With Barrow trailing by 12 points they were still on course for a crucial bonus point, but they began taking points whenever they could: Rooney added two penalties and two drop goals to cut the gap to six.
The Raiders then levelled matters at 22-22 when Chris Young crossed and Rooney converted, but Sheffield still wanted all three points and Craig Cook’s drop goal edged the home side back into the lead.
Cook then sealed the Eagles’ win with a try just a minute from time, Woodcock adding the conversion.