US benchmark West Texas Intermediate for April delivery jumped $1.35 to $35.92 a barrel on the New York Mercantile Exchange.
In London, Brent North Sea crude for May delivery, the European benchmark for oil, finished at $38.72 a barrel, up $1.65.
WTI notched a gain of roughly $3 over the week, while Brent was up more than $3.5.
It was the second consecutive week of solid gains on the oil market, which had wallowed near 13-year lows below $30 a barrel in January as the persistent global oversupply appeared likely to stretch into the distant future.
"We're seeing a lot of investors coming back and working to the upside again," said Carl Larry of Frost & Sullivan.
On Friday, "we're riding on the back of the (US) unemployment numbers," he said, referring to the Labor Department's closely watched monthly jobs report.
Job growth was much stronger than expected in February and the unemployment rate held at 4.9 percent, an eight-year low.
The surprising strength in the job numbers "does underline decent economic growth," thus boosting the demand outlook, said Kyle Cooper of IAF Advisors.
Some analysts pointed out that behind the jobs number were other less-positive details, such as a slight drop in wage growth and a stubbornly high number of part-time employees.
From the oil market's viewpoint that does not matter, Larry said. "If it's full-time workers or part-time workers, it's still workers that have to drive to work."
The latest US oil rig count from Baker Hughes offered a signal of reduced US crude production. Data from the oilfield service provider showed the number of active rigs dropped by 13 to 489, down 60 percent from a year ago.