Raul Jimenez gave Wolves a first-half lead when he netted his seventh goal of the season from Adama Traore's cross.
Andrea Belotti pulled one back shortly after half-time but Leander Dendoncker restored Wolves' advantage just a minute later when he side-footed home a rebound from Diogo Jota's saved shot.
Both teams had chances late on but Wolves saw it through for a fairly comfortable victory.
Six Europa League qualifiers played, six victories registered and 19 goals scored.
It may have disrupted their pre-season preparations a tad and maybe got in the way of their early league fixtures, but when Wolves look this good in Europe it's surely just a small price to pay, writes Tim Spiers at Molineux.
Nuno Espirito Santo's team breezed past minnows Crusaders and Pyunik but in Torino they were offered a stern test, with last season's seventh-placed Serie A side capable of derailing their European adventure.
However, Wolves made mincemeat – or should that be bolognese – of the Italians, whose hopes of winning were pasta joke without their finishing boots.
To be fair, Torino pushed Wolves close over the two legs. If they'd scored the opening goal in Turin instead of hitting the bar, or made their early pressure count at Molineux here, or made it 5-4 on aggregate with one of their two late chances, it could have been a different story.
Wolves, though, fully deserved their hard-earned victory. They weren't at their best here, but they were both professional and clinical and also managed the game better than they had in Turin, as per Nuno's pre-match request. They could also rely, once again, on the heroics of Adama Traore (four assists) and Raul Jimenez (seven goals) who, along with Rui Patricio and Willy Boly, have made exceptional starts to the campaign.
The likes of Roma, Porto, PSV, Sevilla and Lazio lie in wait for tomorrow's draw.
Who knows where this wonderful Wolves journey will take us next, but on this showing there could be plenty more special nights ahead in Europe this season. Who would have said that two years ago?
Nuno reverted to the XI which had won 3-2 in Turin a week earlier, except Jonny Castro Otto came in for the bench Ruben Vinagre. Matt Doherty, as in Turin, wasn't included in the squad.
Torino arrived at Molineux surely needing to score the first goal to have a realistic chance of progressing through to the group stages. And, in the early stages, they threatened to do just that with Wolves struggling to get out of first gear.
Midfielder Daniele Baselli tried his luck with an ambitious volley from a corner, Paul Scholes-style, but that didn't trouble Rui Patricio in what was the theme of the opening 20 minutes – Torino arguably the more threatening side but unable to bother the keeper.
A free-kick bounced just wide after skimming off a Torino head and then Tomas Rincon caused serious concern with a firecracker of a volley which flashed past the post.
Wolves were continuously conceding possession, often in their own half, with Adama Traore the chief culprit, while Jesus Vallejo endured a really poor first-half in which the Spaniard was often hesitant and could barely find a gold shirt with a pass.
Nuno's team desperately needed an injection of life – and it came via Traore who embarked on an explosive dart into the box, searing past two helpless defenders who could only watch as he teed himself up for a low shot which was blocked by keeper Salvatore Sirigu.
From that moment onwards Wolves were on the front foot. Diogo Jota saw a shot blocked and a couple of promising attacks came to nothing as questions were suddenly asked of the visitors.
Then came the game's pivotal moment – via two familiar sources. Traore, after good work from Wolves' best player in the first half, Willy Boly, picked his moment to surge past his man and then cut back onto his left foot to swing over a low cross, which was cleverly diverted in at the near post by Raul Jimenez.
It was Traore's fourth assist in seven appearances this season – and Jimenez's seventh goal from just nine matches.
Wolves were given another scare soon after when Simone Zaza got up above Conor Coady to head goalwards from Lorenzo De Silvestri's cross, but he put his header too close to Patricio who made a comfortable save.
That was it for the half, with Wolves in complete control with 45 minutes remaining and Torino needing to score three goals to advance.
The Italians had to go for it and they started the second half intent on doing just that, with Patricio smartly pawing a Baselli free-kick out from the top corner.
They then levelled things up on the night and made it 4-3 on aggregate when the dangerous Andrea Belotti diverted Baselli's powerful inswinging free-kick past Patrico with what looked like a training ground routine enacted perfectly.
Undeterred, Wolves immediately restored their two-goal advantage on aggregate when, after Jota found space to test keeper Sirigu via a sharp burst of pace, Leander Dendoncker cleverly side-footed the rebound home from 18 yards, in off the post.
While that put Wolves back in front on the night the situation changed little for Torino – they still needed to score two goals to progress.
Wolves looked to close the game out, with Traore behind most of their sporadic attacks as he gave Temitayo Aina a torrid time down the flank.
The hosts were comfortable enough for the fans to give it the old 'ole' as they controlled possession. They were given a couple of late scares with substitute Soualiho Meite curling wide from a superb position and then Belotti firing wide after wriggling past Coady. In between Dendoncker almost added a second but his effort from 10 yards was blocked by Sirigu.
Torino had their moments. But Wolves were just too good.
19 - Torino have started very much the brighter of the two teams. Rincon lets fly from the edge of the box, and his thunderous volley flashes inches wide of the far post. Wolves have looked nervous.
30 - GGGGOOOALLLLLL! Wolves are ahead! Wing wizardry from Traore, with his low cross being tapped home by Jimenez. Traore toys with Aina and perfectly picks his moment, and Wolves' No.9 does the rest in typically exceptional style. And breathe.
37 - Hold on, a chance for Torino - a big one too. Zaza rises above Coady to meet a cross from the right, but his header lands in the grateful hands of Patricio. Should have scored.
58 - Goal! Torino pull one back. Baselli whips a powerful free-kick into the danger zone, and Belotti meets it well with his head to put the ball past the helpless Patricio.
59 - GGGGGOOOOOOAAALLLLL!! An immediate response from Nuno's side! Jota breaks through and has his low strike kept out by Sirigu, but the ball falls kindly for Dendoncker, who slots it home via the post.
87 - Meite almost makes it an anxious final few minutes as he tries his luck from the edge of the box, but his right-footed curler goes just wide. The Torino substitute cuts a frustrated figure.
Wolves (3-5-2): Patricio; Vallejo, Coady (c), Boly; Traore, Saiss, Dendoncker, Moutinho (Neves, 90), Otto; Jimenez (Neto, 90+2), Jota (Cutrone, 81)
Subs not used: Ruddy (gk), Bennett, Vinagre, Gibbs-White
Goals: Jimenez (30), Dendoncker (58)
Torino (3-5-2): Sirigu; Izzo, Bremer, Bonifazi; De Silvestri, Baselli, Rincon (Meite, 72), Lukic, Aina (Berenguer, 70); Zaza (Millico, 81), Belotti (c)
Subs not used: Rosati (gk), Singo, Parigini, Djidji
Goal: Belotti (57)
Wolves are away at Everton on Sunday, kick off 2pm.