Jimmy Smith headed Slade's men ahead in the 35th minute, but the Swans levelled on the stroke of half-time through Cedric Van der Gun.
The real drama was still to come as home defender Alan Tate diverted a cross from substitute Paul-Jose M'Poku into his own net, but Jones impressed throughout with several fine saves.
Slade said: "I'm very proud we have managed to get to the last 16 of the FA Cup.
"It's a great competition especially for lower league sides and we will carry the flag for League One.
"It was a good defensive display and I knew before the game that Jamie was going to have to make saves. I was pleased with his performance and he made good saves."
Source: PA
Source: PA