Certainly Mick McCarthy will be wondering how his side lost a game that they had dragged themselves back into in the second-half, only to throw it all away again.
Darren Bent had given the Black Cats the lead from the spot on nine minutes when it had seemed Segundo Castillo had actually got his foot to the ball.
Steve Bruce's men were two up when they were awarded another penalty this time converted by Kenwyne Jones three minutes after the break.
But just as they did against Burnley last week Sunderland contrived to throw away a lead as an own goal from John Mensah and a Kevin Doyle effort had Wolves level on 55 minutes.
However unlike last week Sunderland responded and goals from Jones and Michael Turner made sure the points were safe before Bent fired in off Michael Mancienne to finish the scoring.
Despite Wolves playing more than 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 Castillo's challenge on Bent sent the striker sprawling and referee Lee Mason pointed to the spot.
Bent dusted himself down before smashing his penalty low to Hennessey's right, and Sunderland were on their way, or so it appeared.
No real chancesIn fact, Bruce's men created only two more chances of note during the remaining of the half, 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 at the break, Jordan Henderson replacing the injured Lee Cattermole and Michael Kightly coming on for Castillo.
But the newcomers 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.
Berra went some of the way to redeeming himself within a minute of his rash challenge when his shot was palmed on to Mensah's chest by Gordon and the ball flew into his own net.
Gift-wrappedBut 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 had no option but to award 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.
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.
SunderlandTeam StatisticsWolverhampton Wanderers5Goals211st Half Goals09Shots on Target51Shots off Target72Blocked Shots87Corners921Fouls132Offsides21Yellow Cards30Red Cards059.4Passing Success62.518Tackles2766.7Tackles Success77.848Possession5244.1Territorial Advantage55.9