The hosts nearly scored after just 20 seconds, Jones missing from six yards, but he made amends 30 minutes later nodding in Dave Brammer's superb cross.
Plymouth piled on the pressure, but Russell's deflected 25-yard strike gave the Potters breathing space.
And Pilgrims midfielder Akos Buzsaky was unlucky to see his 25-yard effort strike the woodwork.
Plymouth boss Bobby Williamson:
"We played some good football at times and had our chances in the first half, but we did lack a spark for most of the game.
"I was also disappointed with the goals we conceded because I didn't think we made Stoke work hard enough for them.
"The players kept plugging away and didn't give up. There is a thin line between success and failure in football these days and this wasn't our day."
Stoke: Simonsen, Buxton, Duberry, Taggart, Hill, Greenacre (Paterson 87), Brammer, Russell, Clarke (Neal 83), Noel-Williams, Jones (Henry 78).
Subs Not Used: de Goey, Ricketts.
Booked: Taggart, Russell.
Goals: Jones 28, Russell 41.
Plymouth: McCormick, Worrell, Aljofree, Coughlan, Dodd, Taylor (Capaldi 70), Buzsaky, Wotton (Lasley 81), Norris, Blackstock, Evans (Chadwick 70).
Subs Not Used: Larrieu, Doumbe.
Ref: C Boyeson (E Yorkshire).