Oxley’s long goal-kick soared over opposite number Darren Jamieson to give his side a commanding 2-0 lead in the first half and they held on for a first victory, despite Declan Gallagher pulling one back for Livingston.
The visitors were inches away from claiming an early opener when Gallagher nodded a corner against the bar, but Farid El Alagui (16) showed more accuracy at the other end, rising the highest to head Hibs in front from a corner.
A dramatic opening to the match was given a comic twist as the hosts’ keeper Oxley (19) added a second goal. There seemed little danger when Oxley unleashed a lengthy clearance, but Jamieson was caught off guard as the ball soared over him and into the net.
Hibs were hungry for more and Jordan Forster fired over, but Livingston nearly pulled one back before the break as Callum Fordyce’s volley was cleared off the line.
Samuel Stanton spurned a chance to increase his side’s lead in the second half, scuffing at goal from inside the box, and Livingston’s Gallagher (60) punished this miss when he prodded in after Keaghan Jacobs’ effort hit the bar.
This setback drew a determined response from Alan Stubbs’ man and El Alagui just failed to get a telling touch to David Gray’s cross, but Livi remained dangerous and Oxley denied Danny Mullen.
In the dying stages, Hibernian were forced to dig deep in defence and they watched with relief as Gallagher’s late effort flew over the bar.