The most actively traded Brent futures, for June delivery, settled up $1.29, or 1.6%, at $79.89 a barrel.
Brent futures for May delivery, which expired upon settlement, gained 50 cents, or 0.6%, to settle at $79.77 a barrel.
West Texas Intermediate crude (WTI) for May delivery settled higher by $1.30, or 1.8%, at $75.67 a barrel, gaining about 9% for the week.
Signs that inflation is slowing tend to support oil prices as this could point to less aggressive interest rate hikes from the Fed, lifting investor demand for risk assets like commodities and equities.
Brent settled lower for the third quarter in a row, the first time that has happened since 2015.