The Black Cats found themselves 2-0 up three minutes into the second half after first leading scorer Darren Bent and then Jones had converted penalties.
That was perhaps a little harsh on the visitors, and John Mensah's own goal and Kevin Doyle's strike inside six second-half minutes were little more than they deserved.
However, what Sunderland lacked in defence, where they were tormented at times by Doyle and Andy Keogh, they more than made up for in attack.
Jones restored their lead with 20 minutes remaining with a powerful long-range drive, and when Michael Turner powered home a 73rd-minute header, the home fans among a crowd of 37,566 were able to breathe a little more easily.
Wolves boss Mick McCarthy's misery was complete in injury time when defender Michael Mancienne deflected Bent's shot past keeper Wayne Hennessey to complete the scoring.