Leicester City, second in the Premier League, beat Wigan Athletic 2-0, Bournemouth beat Luton Town 4-0 and Portsmouth won 2-1 at Fleetwood in the day's other late kickoffs in the FA Cup.
Holders Manchester City began their assault on the FA Cup with a 4-1 victory over fourth-tier Port Vale but Manchester United and Wolverhampton Wanderers face an unwanted replay after drawing 0-0 at Molineux on Saturday.
Goals from Oleksandr Zinchenko, Sergio Aguero, Taylor Harwood-Bellis and Phil Foden made it a routine day for City, although Tom Pope had equalised for a Vale side sitting 74 places lower in the standings.
Manchester United, like City, made multiple changes to their starting lineup at Wolves in a tie that never caught fire.
United failed to land a single attempt on target although Marcus Rashford struck the bar before Matt Doherty had a goal ruled out for Wolves.
Leicester City, second in the Premier League, beat Wigan Athletic 2-0, Bournemouth beat Luton Town 4-0 and Portsmouth won 2-1 at Fleetwood in the day's other late kickoffs.
Earlier, third-tier Rochdale held Premier League Newcastle United to a 1-1 draw with 40-year-old substitute Aaron Wilbraham grabbing a late equaliser at Spotland.
Goals by Connor Jennings, Emmanuel Monthe and a late Paul Mullin penalty earned third-tier Tranmere Rovers an unlikely 3-3 draw at Watford after they trailed 3-0 at halftime.
There were two top-flight casualties. Last season's beaten semi-finalists Brighton & Hove Albion went down 1-0 at home to Sheffield Wednesday and Aston Villa lost 2-1 at Fulham.
As has become customary in the FA Cup, Watford and Villa both nine changes to their starting lineups, one less than Southampton who avoid an upset as they beat Huddersfield 2-0 to reach round four.
Although the FA Cup has lost some lustre, Port Vale's Pope provided one of the day's memorable moments.
When Zinchenko's long-range effort put Manchester City in front the floodgates looked set to open.
Instead, the 34-year-old Pope powered a thumping header beyond Claudio Bravo from David Amoo's cross to spark wild scenes of celebration among Vale's 8,000 visiting fans.
They were only level for seven minutes, however, before Aguero finished off good work by Foden.
City needed a VAR intervention to have Harwood-Bellis's goal ruled legal, the youngster deflecting in John Stones's shot despite initially being ruled offside before Foden completed the scoring.
Vale manager John Askey said his team were "fantastic".
"I was worried before the games that teams have come here and got annihilated," he said. "When our goal went in you started to dream a little bit."
Wolves, playing their 36th game of a marathon season, will have another match to prepare for after their stalemate with a United side who face neighbours Man City in the League Cup semi-final first leg on Tuesday.
Both sides lacked intensity in the first half in which the only save was Sergio Romero's from Doherty's rasping volley.
There was more urgency after the break and Rashford almost made an immediate impact when his shot was blocked by Wolves' Conor Coady and looped against the woodwork.
Raul Jimenez hit the outside of the post for Wolves and Doherty's goal was disallowed after his header went in off his arm, but excitement was in short supply.
Despite the fixture pile-up, United manager Ole Gunnar Solskjaer said he was happy with the draw.
"I'm happier to be in the replay than going out -- it's a tough place to come," he said.
Leicester, also in League Cup semi-final action next week, made 10 changes to the side who won at Newcastle on New Year's Day. They needed an own goal by Wigan debutant Tom Pearce to go ahead before Harvey Barnes added their second.
