City reacted by scoring through Sergio Aguero, youngster Taylor Harwood-Bellis — who deflected in a shot from Stones — and Phil Foden as the holders made a successful start to their Cup defence with a 4-1 win.
"Before the game, I was worried that teams have come here and been annihilated but I'm sure the fans are proud of the team," said Port Vale manager John Askey, whose players were invited into City's changing room after the game and took selfies.
"We rode our luck a little bit at times. When that goal [from Pope] went in, you start to dream a little bit."
It was a gentle warm-up for City ahead of a derby against Manchester United in the first leg of the League Cup semifinals next week. United had a much more gruelling test, against Wolverhampton away, and fought to a 0-0 draw that necessitates a replay on January 14 or 15.
It adds to the fixture congestion at the start of 2020 for United, who have to play five games in the league, two in the League Cup and potentially three in the FA Cup from January 1 to February 1.
Marcus Rashford struck a shot against the crossbar soon after coming on as a substitute, while Wolves later had a goal by Matt Doherty ruled out for hand ball.
"I'm happier to be in the replay than going out," United manager Ole Gunnar Solskjaer said. "It's a tough place to come."
Whether Villa and Brighton will be too disappointed with their FA Cup exits is open to question.
Survival in the lucrative Premier League is their first priority and that is far from guaranteed, with both teams within four points of the relegation zone.
Semifinalists last year, Brighton fell at the first hurdle this season after losing 1-0 at home to second-tier Sheffield Wednesday because of Adam Reach's 65th-minute winner.
Villa are now four years without a victory in the FA Cup after losing 2-1 at another second-tier opponent in Fulham, who scored long-range goals through Anthony Knockaert and Harry Arter.
Arter's stunning 74th-minute winner came two minutes after he came on as a substitute.
Watford's resurgence under new manager Nigel Pearson — three wins in four games igniting Premier League survival hopes — looked like being transferred to the FA Cup when they took a 3-0 lead after 34 minutes against third-tier strugglers Tranmere Rovers.
Then the early-season version of Watford returned. After conceding goals in the 65th, 78th and 87th minutes, the hosts had Argentina midfielder Roberto Pereyra sent off in the 89th minute and ended up scraping a draw.
Another team taken to a replay by third-tier opposition were Newcastle, who also squandered a halftime lead and drew 1-1 at Rochdale.
Aaron Wilbraham, a 40-year-old striker whose first career goal came in 1998, scored Rochdale's equaliser against Newcastle, who have not gone beyond the fourth round since 2006.
A replay was the last thing Newcastle or Watford needed after playing four games in 11 days over Christmas and the New Year. Newcastle, in particular, were hit hard by injuries during the festive period and picked up two more at Spotland, with scorer Miguel Almiron (groin) and Yoshinori Muto (hip) forced off.
Leicester, second in the Premier League, were among the top-flight teams to make wholesale changes for the Cup but it didn't stop Brendan Rodgers' side beating second-tier Wigan 2-0 thanks to an own goal and a strike by Harvey Barnes.
Burnley, Southampton, Norwich and Bournemouth also avoided upsets with some ease to book their places in the fourth round. Burnley beat third-tier Peterborough 4-2, with striker Jay Rodriguez scoring twice, Southampton defeated second-tier Huddersfield 2-0 and Norwich won 4-2 at Preston, with Irish striker Adam Idah scoring a hat-trick. Bournemouth beat second-tier Luton 4-0.
A one-minute delay preceded all third-round games to raise awareness of a mental health campaign, "Heads Up," which is spearheaded by English Football Association president Prince William.
- AP
