The Lady Cougs didn't help themselves any by making some un-timely errors, spoiling another excellent outing in the circle from ace Sarah Taylor.
Taylor worked all seven innings and gave up just six hits while fanning 12, walking one and hitting one.
Bradley picked up a pair of runs in the top of the first inning on an infield hit and an error.
The damage could have been worse, but Taylor ended the frame with a big strikeout, leaving runners on second and third.
The Lady Cougars were retired in order the first three innings but did have a shot at scoring in the home half of the fourth.
Taylor led off with an infield hit and then she motored from first to third on a fielder's choice by Brittany Shrable.
But Taylor was left at third as Bradley got out of the inning with a line-out and strikeout.
The Lady Bears really put the pressure on Izard County by crossing the plate four times in the top of the sixth.
The first run came home on a passed ball, but the big blow was a triple that ended up plating three runs, thanks in part to a throwing error.
Down 6-0 after five-and-a-half innings of play, Izard County finally had a productive stretch in the bottom of the sixth.
Kayla Townsend reached first on an error and after a strikeout, Taylor got on board with a base-on-balls.
Harmony Herron joined Townsend and Taylor on the base paths with a hit past third base, loading the bases for Izard County.
Kristen Doty came through by sending a ball into left field that was dropped, scoring Townsend and Taylor on the play to make it 6-2, Bradley.
Taylor struck out the side 1-2-3 in the top of the seventh to give the Lady Cougars one last chance in the bottom of the frame.
Townsend hit safely to right in the home half of the seventh, but that was it for Izard County and Bradley advanced to the second round with a 6-2 victory.