Jones, who could have had a hat-trick, tormented the Millwall defence all game and added a much needed attacking edge to the lowest scoring team in the Championship.
The visitors took the lead after 15 minutes through on-loan Southampton striker Jones, who scored seven goals in as many games during a recent loan spell at Sheffield Wednesday after.
The Potters man out-jumped the static Millwall defence to head home a cross from fellow debutant, Kevin Harper, past Andy Marshall and into the goal.
He should have doubled the lead ten minutes before the break when he was again unmarked, but this time he headed Chris Greenacre's cross straight into the grateful arms of Marshall.
During the intervening half hour the Lions picked up their game, but both Danny Dichio and Scott Dobie were guilty of poor finishing.
Barry Hayles thought he had levelled things on 25 minutes only to be ruled offside by the linesman.
Millwall pressed after the break and the visitors struggled to get the ball out of their own half.
Second half substitute Peter Sweeney had a golden opportunity on the hour to equalise with a free-kick from the edge of the box, but his shot hit the wall and went behind for a corner.
While the home side pressed they were always open to the sucker-punch and Jones again came close with ten minutes left, this time firing wide from just inside the box.
Despite a late rally Millwall were unable to take a share of the points and the result leaves their play-off hopes in doubt.