Spudding had been delayed by about two weeks, after bad weather in the region prevented the rig from leaving the previous well, Frankland-1.
At 6am on Friday, Roc said the well was drilling ahead a depth of 107m.
Perseverance-1, the second in a three-well program, is in WA-325-P, about 100km northwest of the joint venture’s Cliff Head oil field.
Drilling is expected to reach a total depth of 1774m by late this week.
Interests in WA-325-P are Roc (37.5%), Apache Northwest (37.5%), Arc (20%) and Wandoo Petroleum (5%).