The former Nottingham Forest forward made sure of a home tie against either Southampton or Lincoln, who replay next week, with goals after 13 and 39 minutes.
Jemson, who also scored Oxford's winner against Sheffield Wednesday in the second round, has now hit four goals in the last three games.
On this occasion, though, he was blessed with good fortune with both goals as Oxford took their tally to nine in their last three home games, all of which they have won.
His first, in the 13th minute, took a wicked deflection off the defensive wall from a 25-yard free-kick which completely wrong-footed the Port Vale goalkeeper, Paul Musselwhite.
Then, six minutes before half-time, Musselwhite allowed a header from Jemson to slip through his hands and into the net.
The visitors, who lost Steve Guppy with a back injury during the pre- match warm-up, created two chances early in the second half, but Lee Mills and Gareth Griffiths squandered both with poor headers to let Denis Smith's side off the hook.
Vale's overall performance did not please their manager, John Rudge. He said: "It was a disappointing performance after the standards we set on Saturday [Vale beat Birmingham City 3-0]. We did fancy our chances after drawing Oxford at home but we didn't play well in either game."
Meanwhile, Smith admitted: "Vale are a good side and they've a good record away from home of late. But we had a bit of luck with the first goal, managed to get the second and then our keeper had to pull off several good saves."
Oxford United: Whitehead; Robinson, Ford, Smith, Elliott, Purse, Angel, Gray, Aldridge (Massey, 80), Jemson, Beauchamp (Rush, 80). Substitute not used: Moody.
Port Vale: Musselwhite; Hill, Tankard, Walker, Griffiths, Glover, McCarthy, Porter, Mills (Foyle, 70), Naylor, Corden (Talbot, 70). Substitute not used: Van Heusden.
Referee: J Kirkby (Sheffield).Reuse content