Winger Simon Hackney produced a four-minute double salvo to give the Cumbrians all three points after substitute Joyce netted in his first game of the season as the hosts came back from 2-0 down.
Joyce's goal - bundled in on the line just three minutes after coming on - finally breathed some life into a Carlisle side, who had performed appallingly in the first half.
Port Vale took the lead on 27 minutes when Adam Eckersley's cross deflected off David Raven and looped to the back post where Danny Glover cut back for Paul Harsley to slide home from four yards.
Amazingly, League One's bottom side added a second 11 minutes later when Mark Salmon's expert pass put Danny Whitaker clean through, allowing him to skip around keeper Keiren Westwood before finishing into the open goal.
Despite Joyce's comeback strike immediately after the break, the Carlisle defence still looked weak, with Peter Murphy making his comeback after seven games out and obviously short of match fitness.
Westwood was then forced to save bravely at Glover's feet with the teenage striker clean through on goal.
But on 65 minutes Hackney brought Carlisle level when striker Danny Graham's chipped pass found him with just keeper Joe Anyon to beat and the flying winger launched a thunderous volley into the top corner from 20 yards.
And four minutes later the home crowd were on their feet as the turnaround was complete with Hackney grabbing his second.
The ex-Liverpool trainee found space at the back post, giving him room to volley Joe Garner's cross into Anyon's far post.
And it was a case of history repeating itself for the travelling Vale fans, who saw their side lose in exactly the same fashion in the corresponding fixture last season.
But although substitute Charlie O'Loughlin went close at the death, the visitors never really looked likely to spark their own fightback.