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.
Spot on: Darren Bent notches his sixth of the campaign with this crisp penalty
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.
McCarthy arrived at the Stadium of Light to try once again to claim a first Barclays Premier League victory on Wearside, something he never managed during his time as Black Cats boss, and he will have headed for the dressing room at half-time with mixed emotions.
Despite seeing his side more than play a part in an entertaining first 45 minutes, they left the pitch at the break trailing to the only goal.
That came just nine minutes into the contest when Segundo Castillo's clumsy challenge on Bent sent the striker sprawling and referee Lee Mason pointed to the spot.
In vain: Wolves players surround referee Lee Mason after the award of the penalty
Bent dusted himself down before smashing his penalty low to Hennessey's right, and Sunderland were on their way, or so it appeared.
In fact, Steve Bruce's men created only two more chances of note during the remaining of the half, Kenwyne Jones forcing a good save from Hennessey 12 minutes before the break and the keeper then plucking Bent's lob out of the air after the ball fell nicely for the former Tottenham frontman six minutes later.
But with Wolves arguably just shading the opening 45 minutes, they had several opportunities of their own.
They were aggrieved not to be awarded a 31st-minute penalty for Turner's untidy aerial challenge on Doyle, who was proving a real handful, while midfielder Dave Edwards twice went close with close-range headers.
Republic of Ireland striker Doyle led a rousing finish to the half by the visitors, twice forcing Turner into good blocks in injury time.
But he came agonisingly close to an equaliser at the death, glancing a header just wide with keeper Craig Gordon beaten.
Both managers made changes a the break, Jordan Henderson replacing the injured Lee Cattermole and Michael Kightly coming on for Castillo.
But the newcomers had hardly had a chance to break sweat when Sunderland increased their lead.
Bent got in front of Christophe Berra to collect Steed Malbranque's low cross and then went over the defender's out-stretched leg, and the outcome was inevitable.
Jones successfully argued his case to be allowed to take the penalty with Bent, and duly dispatched it past Hennessey.
However, what looked like a commanding lead dissolved within six minutes.
Double trouble: Kenwyne Jones scores from the spot to put Sunderland 2-0 up
Berra went some of the way to redeeming himself within a minute of his rash challenge when his cross was palmed on to Mensah's chest by Gordon and the ball flew into his own net.
But if there was an element of misfortune about the goal, the equaliser was gift-wrapped.
Kieran Richardson's miscued back-pass might have ended up in the net had Gordon not got a hand to it, but Mr Mason awarded a free-kick six yards out.
Karl Henry's shot from Keogh's tap was blocked, but Doyle gleefully thumped the rebound home to get his side back on terms.
The game was back in the melting pot with Wolves sensing a chance to claim back-to-back league wins and Sunderland defending with a distinct lack of confidence.
False dawn: Kevin Doyle pulls Wolves level
However, when they finally responded, they did so in devastating fashion.
Jones demonstrated his potency with 20 minutes remaining when he drilled a low shot past Hennessey and into the bottom corner to restore his side's lead, and although the keeper pulled off a fine save to deny Bent three minutes later, he was beaten again within seconds.
Turner, whose header against former club Hull was eventually given as an own goal, made sure there was no argument this time with a well-placed downward header from Andy Reid's corner to make it 4-2.
Richardson had to clear Greg Halford's 76th-minute header off the line to deny the visitors another lifeline, but Mancienne's late contribution rubbed salt into the wound.
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