Nuno's men picked up their first clean sheet in the league since the 2-0 win over West Ham at the start of December at Old Trafford.
And it was no coincidence that the shut-out coincided with Boly's return from a broken fibula.
Though Wolves would have keeper Rui Patricio to thank for the point as he stopped Portugal team-mate Bruno Fernandes from making a dream debut for United.
Nuno had made two changes from the side that lost 2-1 to Liverpool earlier this month.
Forward Diogo Jota (calf) and defender Boly (ankle) were only fit enough to start on the bench against the Reds.
But Boly made first appearance since breaking his fibula in October, with Jota back from a dead leg sustained at Watford on New Year's Day.
Wolves started in their standard 3-4-3 shape with United taking on a 4-2-3-1 formation.
The Red Devils gave Bruno Fernandes his debut in the middle of the park with Wolves' new Portuguese ace Daniel Podence starting on the bench.
Wolves had the first chance of the game when a Joao Moutinho corner landed awkwardly for Romain Saiss in the box.
The centre-half as given time and space to recover but eventually blasted the ball wide after spinning in the box.
Jota was Wolves' danger-man in the opening exchanges as he looked fresh on his return and his form on the left allowed pockets of space for Traore on the right.
But Wolves could not find a way past David De Gea.
Up the other end Boly slotted in seamlessly with Coady making a number of key interceptions.
Wolves contained United to just the one effort from distance as Andreas Pereira fired wide.
And they should have opened the scoring in the 20th minute as Doherty's looping header from a Moutinho corner sailed towards goal.
But De Gea was on hand to bat the ball away.
Doherty was nearly instrumental in Wolves opening the scoring as his delightful one-two with Neves saw him slice open United.
But as the ball fizzed towards Jimenez in the six-yard box United just extinguished the danger.
Daniel James and Juan Mata had caused Wolves problems in the 1-0 FA Cup defeat.
But Wolves managed to contain the duo in an evenly matched first-half.
Maguire saw an effort from distance fly to safety and Jonny saw a penalty shout waved away after he tangled with Wan-Bissaka in the box.
Wolves kept pressing as the half wore on with Traore thundering the ball into the stands.
Wolves had conceded first in 17 of their previous Premier League matches and Fernandes was given a golden opportunity to make his mark on debut.
Wolves failed to clear and the midfielder was left unmarked at the top of the box.
But his fellow countryman Rui Patricio was on-hand to stop his strike.
Wolves started the second half on a high note with Diogo Jota finding gaps in United's defence.
The forward tangled with Maguire as he danced into the box but as De Gea collected the ball referee Paul Tierney waved away the Wolves man's penalty claim.
But United fought back up the other end with Neves booked for fouling Mata.
It gave Fernandes a dead ball opportunity just outside the box but Patricio once again stopped his hopes of a debut goal.
Mata's strike sailed past the right post after Wan-Bissaka had opened Wolves up as United started to dominate.
Wolves boss Nuno cast a frustrated figure on the sidelines and he was shown a yellow card by Paul Tierney.
The hosts kept asking questions with Fernandes' strike too hot for Patricio to handle as he failed to keep the ball in play.
But one of Wolves' strength is the counter-attack and as United pushed forward it gave Traore more freedom to use his electric pace.
The forward burst from his own half and bypassed five red shirts before releasing Jimenez on the right.
He sprinted through on goal at an angle and only De Gea's fingertips stopped Wolves taking the lead.
Jota made way for Neto and Traore would soon go off after receiving treatment on the pitch for a left ankle knock.
And that paved the way for Podence to make his debut.
Patricio made a fine instinctive top to thwart Mata after he diverted Mason Greenwood's long-range effort towards goal.
But Wolves went straight up the other end with Saiss nodding a Moutinho set-piece off target.
Podence made his mark as the clock ticked down as he linked-up with Neves and Doherty on the right to conjure something out of nothing.
His cross from the right whirled towards Doherty at the near post but his effort was deflected out for a corner.
United kept the heat on at the other end of the pitch with Nuno making a defensive substitution as the clock ticked down.
Dendoncker entered the fray in his normal midfield role with Neto and Podence finishing the game in a front two.
And United should have won the game at the death as Diogo Dalot nodded Wan-Bissaka's cross from the right just off target.
But Wolves held on to a 0-0 draw that could be the springboard for a special second-half of the campaign.
35 - Thought the net was going to bulge there. Traore lets fire from the edge of the box, and it fizzes just off target. He scored from that position against both Tottenham and Man City at Molineux.
52 - Almost! Jota goes on a sensational jinking run and looks like he is going to pull the trigger from close range, but he is off balance and cannot get the shot off. Shame that.
60 - A warning for Wolves. Mata is allowed to turn on the edge of the area, and he looks to find the bottom corner with his left foot. The shot goes inches wide of the post.
78 - Top reactions from Patricio to keep it goalless! Greenwood has a crack from distance, and it takes a wicked deflection off Boly, but the Portuguese shifts his body back the other way to make the save.
90 - Close! Dalot puts a header a fraction wide of the post for United in the dying seconds of the clash. The substitute cannot believe he has not scored. Wolves breathe a big sigh of relief.
United (4-2-3-1): De Gea; Wan-Bissaka, Lindelof, Maguire (c), Shaw; Fred, Pereira (Greenwood, 72); Mata (Lingard, 88), Fernandes, James (Dalot, 88); Martial
Subs not used: Romero (gk), Jones, Williams, Chong
Wolves (3-4-3): Patricio; Boly, Coady, Saiss; Doherty, Moutinho, Neves, Otto; Traore (Podence, 76), Jimenez (Dendoncker, 90), Jota (Neto, 70)
Subs not used: Ruddy (gk), Kilman, Jordao, Gibbs-White
Referee: Paul Tierney (Lancashire)