England, appearing in their first semi-final since 1990, had looked on course for their first final since 1966 as they led through Kieran Trippier's fifth-minute free kick and totally dominated the opening half.
Ten-man Arsenal suffered a 3-0 Premier League defeat at Leicester City on Sunday in another blow to their hopes of finishing in the top four and qualifying for the Champions League.
City have 89 points, one more than rivals Liverpool, with both teams having three games to play -- and none of them against top six opponents.
Manuel Pellegrini has said he would choose winning the Premier League with Manchester City and being shown the door over continuing as the team's manager for an extended period without any major success.
Holders Real Madrid breezed into the last 16 of the Champions League with two games to spare when a Karim Benzema strike secured a 1-0 win in their Group B match at home to a toothless Liverpool on Tuesday.
City, who have dished out a string of maulings in a stellar league campaign, found the Championship side a tough nut to crack and had to wait until the 92nd minute to grab the winner when Argentine substitute Aguero darted in to head home.
Manchester City opened up a two-point lead over their neighbours Manchester United at the top of the English Premier League on Saturday thanks to another display of scintillating brilliance in a 7-2 thrashing of Stoke City at the Etihad Stadium.
News of all that's transpired on and off the football field
Images from Sunday night's English Premier League matches.
News of all that's transpired on and off the football field
Liverpool continued their perfect start to the season to stay top of the Premier League after a goal in each half gave them a 2-1 victory over Tottenham Hotspur at Wembley on Saturday.
England have what it takes to get the better of any opponent but need to be consistent if they are to win their first European Championship in France, captain Wayne Rooney has said.
Liverpool's 1-0 defeat by Aston Villa on Saturday was more than an early season setback - it raised the question of whether they have the strength in depth to cope with the dual challenge ahead of them this term.
Having left it late to earn a 3-2 win in the first leg, City took a while to hit their stride at The Etihad on Tuesday but when they did Guardiola's team produced a magnificent attacking display that will ring alarm bells around Europe.
'We can work and fight for it' 'Yes, they had much more of the ball. Yes, they had that apparent control of the game but the biggest save is the double save of their goalkeeper and the biggest decision of the game is the unlucky decision of Michael (Oliver)'
Raheem Sterling scored a second-half hat-trick as leaders Manchester City beat Watford 3-1 on Saturday while Liverpool kept the gap at one point by overcoming Burnley 4-2 on Sunday.
News of all that's transpired on and off the football field
Goals rained in for Manchester City and Manchester United but Juergen Klopp's first game in charge of Liverpool was solid rather than spectacular with his new side drawing 0-0 at Tottenham Hotspur in the Premier League on Saturday.
Rooney's 50th, 150th and 200th EPL goals have all come against Manchester City.
IMAGES from the Champions League matches played on Wednesday.
Manchester City strengthened their Premier League top-four aspirations with a 5-0 thrashing of a woeful Crystal Palace side at the Etihad Stadium on Saturday.
Goals rained in for Manchester City and Manchester United but Juergen Klopp's first game as Liverpool manager was solid rather than spectacular as they drew 0-0 at Tottenham Hotspur in the Premier League.
Luka Modric pulled one back for Zinedine Zidane's shellshocked side with a brilliant strike from distance early in the second half before substitute Vinicius Jr reduced the deficit to one goal.
News of all that's transpired on and off the football field
'My hope for Rashford, and it is a vain hope, is that he will be allowed to develop in peace and it won't suddenly be a question of, 'You have scored two goals for Man United and you're going to be the next Cristiano Ronaldo' or every time he has two or three bad games he is a flash in the pan'
Liverpool manager Brendan Rodgers has expressed his delight with Christian Benteke and Roberto Firmino after the forwards made their first-team debuts in the club's final warm-up match before the new Premier League season.
Champions Chelsea have not enjoyed the best of starts at home this season and face their biggest test yet on Saturday with the visit of free-scoring leaders Manchester City.
Liverpool took a giant step towards their first title in 24 years with a 3-2 win at a plucky Norwich City on Sunday, opening up a five point lead over second-placed Chelsea with three matches remaining.
Leicester City were give a Premier League reality check when the unlikely leaders lost 1-0 at Liverpool on Saturday after Manchester United slumped to a third consecutive league defeat to pile more pressure on manager Louis van Gaal.
Liverpool surrendered a two-goal lead as they were held to a 2-2 draw by third-tier Shrewsbury Town in the FA Cup fourth round on Sunday after second-half substitute Jason Cummins struck twice to inject some much-needed late magic into the competition. Earlier, Harry Maguire's thunderbolt for Manchester United started a goal rush at Tranmere where the Reds scored five times before halftime. Diogo Dalot, Jesse Lingard, Phil Jones, Anthony Martial and Mason Greenwood also scored.
Wayne Rooney celebrated his 100th England cap by scoring a penalty to lead his team to a 3-1 win over Slovenia in a Euro 2016 Group E qualifier at Wembley on Saturday which only came to life after halftime.
An Eden Hazard hat-trick swept Chelsea back to the top of the Premier League on Saturday when they beat Newcastle United 3-0 at Stamford Bridge after previous leaders Arsenal were thrashed 5-1 at Liverpool.
VfL Wolfsburg reached the Champions League last 16 and dealt a knockout blow to Manchester United with a 3-2 victory to claim top spot in Group B and condemn their opponents to the Europa League on Tuesday.
The win moved Spurs up to third but unbeaten Manchester City still looked in a class of their own at the top as Leroy Sane scored twice in a 4-0 stroll over West Ham United.
Three matches into the Premier League season following a stunning title success by 5,000-1 outsiders LeicesterCity, the table already has a more familiar look.
Images from the English Premier League matches played on Sunday
Gabriel Jesus came off the bench to secure Manchester City a 1-0 English Premier League victory at Leicester City after yet another penalty miss by Pep Guardiola's side on Saturday. Chelsea's Olivier Giroud and Marcos Alonso returned to the starting lineup to stunning effect by grabbing a goal apiece in a crucial 2-1 home win over Tottenham Hotspur in the battle between the London rivals for fourth place.
Photos from the Euro 2016 qualifying matches played across Europe on Saturday
Images from the English Premier League matches played on Wednesday
