Ole Gunnar Solskjaer's side had suffered FA Cup KO at the hands of Nuno Espirito Santo's Old Gold in the quarter finals last term, but - this time - at least ensured our name will be in the hat for the fourth round.
The replay means that United's only solitary spare week in January has been filled amid a manic run of 22 games in 60 days.
With the defeat at Arsenal still fresh in the memory, and a League Cup tie with Manchester City in three days time, there was an unfamiliar look to the United side as Solskjaer opted for a mix of youth and experience. Brandon Williams, Tahith Chong and Mason Greenwood all started whilst Ashley Young, Juan Mata, Nemanja Matic and Andreas Pereira also featured.
In a repeat of last year's quarter final, clear cut chances were at a premium, substitutes Marcus Rashford and Raul Jimenez both struck the woodwork after half time.
Rashford came close shortly after coming on in the 70th minute when his deflected effort looped off Connor Cody and against the bar.
Jimenez set himself up as he chased his own header, burst clear and wriggled through before he clipped the crossbar from a tight angle.
Wolves carved out the best chance of the first half when a Pedro Neto corner was flicked on by Leander Dendoncker to Matt Doherty, and his instinctive header was kept out by a brilliant reflex stop from Sergio Romero.
United's Argentine keeper was called into action again soon afterwards when Neto collected the ball from the lively Adama Traore, only for Romero to block with his feet.
Solskjaer's men had a penalty appeal waved away when the impressive Brandon Williams went down under the attentions of Dendoncker, but VAR showed that Williams was going down anyway and had kicked the leg of his opponent.
Mata put a free-kick narrowly wide and Rashford then hit the bar before Wolves thought they'd taken the lead.
Substitute Joao Moutinho did well down the left and picked out Doherty, he headed in but replays - and VAR - confirmed the wing-back had nodded the ball onto his arm before scoring so the goal was correctly ruled out.
Romero saved well again to repel Jonny's low effort, and Harry Maguire then put in a thunderous challenge on Traore. The ball found its way to Pereira via Fred but rather than drive forward he opted to turn square with a slow pass and the chance was gone. It rather summed United's solid if unspectacular display.
The replay will be at Old Trafford between the next two rounds of league fixtures and comes after both clubs - still in the Europa League - have busted a gut over Christmas and New Year. Neither side really wanted another game but at least we're still in the cup.
Overall team performance: 6/10
United Faithful Man of the Match: Brandon Williams