Victory for Pep Guardiola's side came a week after the Premier League trophy was retained to join the League Cup and Community Shield already in City's possession.
Watford reached its first final in 35 years as they came from behind to beat Wolves 3-2 at Wembley.
No English team has ever swept the Premier League, FA Cup and League Cup, let alone win European soccer's top prize at the same time.
On a contrasting Saturday for the two rivals, City came from two goals down to defeat second-tier Swansea 3-2 in the quarterfinals while United went down 2-1 at Wolves.
A rematch of last year's final won by Chelsea, Herrera put United ahead in the 31st minute and Pogba came through just before halftime to double the lead.
"It was the worst conditions I have played in," Foden said. "We had to show professionalism and keep the ball moving and they tired in the end."
Defending champions Chelsea were boosted by two video reviews in beating Sheffield Wednesday FC 3-0.
Connor Wickham and Andros Townsend scored for Crystal Palace in their 2-0 win over Tottenham Hotspur in the fourth round of the FA Cup.
Kevin De Bruyne scored one and had a hand in two others, with Gabriel Jesus, Bernardo Silva and Sergio Aguero scoring along with an own-goal.
The forward's fifth goal in 33 appearances since leaving Arsenal a year ago set United on its way to a 3-1 victory on Friday that booked a place in the fifth round of the FA Cup.
In other all-English Premier League matchups in Monday's draw, Crystal Palace host Tottenham, and Manchester City will be at home to Burnley.
Klopp, who also used the wind as a reason for his team's below-par display at Molineux, has yet to progress beyond the fourth round of the FA Cup in his four seasons in charge of Liverpool.
Fabregas has been linked with a move to French team Monaco, which is coached by former Arsenal teammate Thierry Henry.
Ole Gunnar Solskjaer became the second Manchester United manager to win his first five games in charge as Juan Mata and Romelu Lukaku scored for United against Reading in their 2-0 victory.
Besides the biggest road victory for the club founded in 1882, it was also its largest margin of victory since beating Wigan Athletic 9-1 in 2009.
Despite the tight turnaround after the World Cup, Manchester City's attacking ruthlessness has not been blunted by fatigue or the English heatwave.
Eden Hazard scored a penalty in the first half to give Chelsea the lead and the winner as Conte pulled off a Mourinho by 'parking the bus' and won the FA Cup after a lacklustre season.
After a poor Premier League season, midfielder Fabregas wants Chelsea to win the FA Cup
Chelsea will meet Manchester United in the FA Cup final after beating Southampton 2-0 in the second semifinal at Wembley Stadium on Sunday with goals from Olivier Giroud and Alvaro Morata.
It was Tottenham's eighth consecutive FA Cup semifinal loss since last winning world football's oldest knockout competition in 1991.
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