Davenport steadied her game enough to overcome a determined Osterloh in the second set and then wore down her opponent to storm into the quarter-finals with her 15th straight victory.
The in-form Davenport has won three straight tournaments in her build up to the U.S. Open and looks on course to pick up a fourth in Cincinnati.
Second seed Vera Zvonareva also advanced, recovering breaks of serve in both sets to beat Italy's Antonella Serra Zanetti 6-4, 7-6.
The Russian struggled with her game, making 14 double faults and 60 unforced errors in the match, but converted on the big points to prevail 7-3 in the second set tiebreaker.
In other matches, Laura Granville upset fifth-seeded Denisa Chladkova 6-1, 6-1 to advance to the quarter-final.
Granville next meets fourth-seeded Frenchwoman Marion Bartoli, who defeated Mara Santangelo 6-4 6-0 on Wednesday, in the quarter-finals.
Seventh seed Flavia Pennetta also reached the last eight with a 6-7, 6-2, 6-4 victory over fellow Italian Rita Grande.
