Wolves were the better side in the contest at Molineux Stadium late on Saturday, but failed to capitalise on their chances and saw what they thought was a goal in the 75th called back for a hand ball, reports Efe news.
Romain Saïss' header from a corner in the 13th minute was deflected away from the net moments before United backup goalkeeper Sergio Romero made an outstanding save to deny Matt Doherty from close range.
Both teams began the match with starters on the bench, but both rolled out their big guns Marcus Rashford for United, Raul Jimenez for Wolverhampton in the second half in pursuit of a goal.
Romero stopped Pedro Nato in the 50th minute, nine minutes before United's Juan Mata fired wide on a free kick. Wolves' Conor Coady dove in the path of a Rashford strike, sending the ball into the cross-bar.
The final chance belonged to Jimenez, whose shot clanged off the bar.
Which club moves on to the next round will be decided in a replay at Old Trafford later this month.
The other Manchester team hosted humble Port Vale at the Etihad. The two-time defending Premier League champions and 2019 FA Cup winners took the lead in the 19th minute with a goal by Oleksandr Zinchenko, only to see Tom Pope equalise for Port Vale.
City retook the lead before the break on Sergio Agüero's goal in the 42nd minute. Taylor Harwood-Bellis, 17, widened the lead to 3-1 before the hour mark and Phil Foden added a fourth in the 76th.
Leicester City, currently second in the Premier League, cruised to a 2-0 win against second-division Wigan.
( With inputs from IANS )