Rodgers was thrown into the action by manager martin Foyle after 75 minutes and his pace and aggression soon upset the Bournemouth defence.
With eight minutes remaining, Rodgers latched onto a headed pass from Craig Rocastle to run clear and shoot past the unprotected Asmir Begovic.
It was no more than Port Vale deserved and in terms of chances they should have won far more easily.
Bournemouth can be thankful the scoreline was not a repeat of last season's 4-0 drubbing and they could not have complained if Vale had put away several inviting opportunities.
The worst culprit was midfielder Danny Whitaker who missed five gilt-edged chances.
The worst came in the second half from 12 yards with the goal at his mercy.
Port Vale introduced David McGoldrick, the Southampton striker signed on-loan until January and who last season played 12 times for Bournemouth in a similar arrangement.
McGoldrick and Whitaker were both denied by good saves from Begovic as the Bournemouth defence was often in disarray.
Bournemouth also had their chances as former England midfielder Darren Anderton ruled the midfield in the first half before tiring in the second.
Garreth O'Connor should have done better in the first half than head straight at Joe Anyon after Anderton had picked him out with a superb centre from the right.
Deadline signing Lee Bradbury should have also have done better and marked his debut with a goal.
But in the 56th minute his header allowed Anyon to get down to his left to make a save, and then nine minutes later he was played clear by Jo Kuffour only to shoot straight at the on-rushing goal keeper.
Deep into injury time Bournemouth should have equalised when the unmarked Josh Gowling had time and room to pick his spot but succeeded only in driving a hasty shot straight at the relieved Anyon.