While there was nothing of note to write home about in the first 30 minutes, Eddie Howe's troops looked the more likely to break the deadlock, but Sam Johnstone was not a busy man in the Wolves goal.
Instead, the Magpies were caught cold at the back as the hosts drew first blood through Lemina, who finished off a terrific counter-attack after an exquisite dummy by fellow midfielder Joao Gomes.
Howe's triple half-time substitution said it all about Newcastle's tepid first-half performance, and star striker Alexander Isak - potentially hampered by a facial injury - was one of the three players hooked during the interval.
Gary O'Neil's men did a good job of keeping their visitors in check approaching the final 15 minutes, only to lose their lead in cruel circumstances, as Schar's long-range drive deflected off of Craig Dawson's head and sailed into the net.
The Magpies' tails were up, and only five minutes later, Barnes - brought on as one of the half-time changes - wanted a slice of the long-range action, bending a magnificent effort into the top corner after cutting inside from the left.
As Wolves huffed and puffed in added time, Nick Pope was called into action to make a terrific full-length save from Matheus Cunha to preserve Newcastle's unbeaten record, as the Magpies moved up to third in the table behind Arsenal and Manchester City.
Meanwhile, a third defeat from four leaves Wolves languishing in the danger zone in 18th place, with just one point to show from their opening four games, but there was some encouragement for O'Neil to take once again.
WOLVES VS. NEWCASTLE HIGHLIGHTS
Mario Lemina goal vs. Newcastle (36th min, Wolves 1-0 Newcastle)
They have been under the cosh for the most part and have seen little of the ball, but Wolves have the lead on home turf, and what a well-worked goal it was!
O'Neil's troops turn defence into attack in the blink of an eye, as a Newcastle attack is snuffed out and the ball is worked to Jorgen Strand Larsen, who beats Dan Burn for both pace and power.
The Scandinavian's ball into the box is on the money for Gomes, but the Brazilian instead produces a lovely dummy to let the ball roll through to the unmarked Lemina, who cannot miss from a few yards out.
Fabian Schar goal vs. Wolves (75th min, Wolves 1-1 Newcastle)
Sometimes, you just have to hit and hope, and Newcastle centre-back Schar gets his reward for following that philosophy!
Reinstated to the starting lineup after his three-game suspension, the Swiss defender has a crack from 25 yards, which takes a wild nick off the head of Dawson and loops into the net over Johnstone's futile reach.
Harvey Barnes goal vs. Wolves (80th min, Wolves 1-2 Newcastle)
There may have been a huge stroke of luck about Newcastle's equaliser, but there was nothing fortuitous about this one, as the Magpies complete their second-half turnaround with a Barnes special.
The winger combines with Joe Willock on the left before cutting inside, skipping away from Larsen and Matt Doherty far too easily in the process, before bending a magnificent long-range effort into the top corner!
Nick Pope save vs. Wolves (90+3 min, Wolves 1-2 Newcastle)
A match-winning moment from Newcastle's goalkeeper! Cunha connects brilliantly with a volley, which is bound for the far corner, but Pope acrobatically springs to his right and gets a hand to the ball at full stretch.
MAN OF THE MATCH - HARVEY BARNES
Barnes was questionably dropped from the starting lineup for Sunday's game after making his mark against Tottenham Hotspur a fortnight ago, but Howe will surely not be making that mistake a second time.
The 26-year-old's outrageous winner had a bit of the Gareth Bale about it - albeit on his right foot rather than the Welshman's trademark left - and even though he spurned a late chance to make it three, that was trivial in the grand scheme of things.
WOLVES VS. NEWCASTLE MATCH STATS
Possession: Wolves 49%-51% Newcastle
Shots: Wolves 12-14 Newcastle
Shots on target: Wolves 5-6 Newcastle
Corners: Wolves 4-7 Newcastle
Fouls: Wolves 17-6 Newcastle
BEST STATS
WHAT NEXT?
Wolves only have two full days to rest up before they go again, as O'Neil's men travel to Brighton & Hove Albion on Wednesday evening for an EFL Cup third-round showdown, three days before a Premier League trip to near neighbours Aston Villa.
In contrast, Newcastle have no midweek commitments to worry about over the next few days and return to action away to Fulham on Saturday afternoon.