Treble-chasing City, who wrapped up the title when second-placed Arsenal were beaten at Nottingham Forest on Saturday, have won 12 successive games in the top flight.
Forward Jack Grealish was asked if City, who were eight points behind Arsenal in late March, have felt invincible over the past few weeks.
"Yeah, we have. It's mad because I spoke to some of the lads and said imagine if someone had said that to win the league we would need to win 12 games in a row," Grealish told Sky Sports, with celebrations still going strong on the pitch behind him.
"I'm not saying I didn't think we could do it but it was going to be difficult, but we have so much talent in this squad and at the moment we just feel unstoppable."
City have 88 points from 36 matches, seven more than Arsenal who have just one match remaining. Frank Lampard's struggling Chelsea side are languishing in 12th spot with 43 points.
"It feels unreal right now, I'm so happy," said City's goal-scoring machine Erling Haaland, briefly ignoring the interviewer to dance.
"The memories I will have for the rest of my life, we have been fighting so hard."
Alvarez scored in the 12th minute for a largely second-string City side, slipping the ball under goalkeeper Kepa Arrizabalaga from a pass by Kyle Walker. He also had another goal chalked off for a handball in the build-up.
Alvarez's winner meant City had scored 100 goals at The Etihad this season, equalling the record - which they set in 2018-19 - for most home goals scored in all competitions in a single season by an English top-flight club.
With nothing on the line on Sunday and two huge games on the horizon - the FA Cup and Champions League finals - City manager Pep Guardiola left his big guns, including Haaland, on the bench for most of the game.
The Spaniard, who claimed his 10th major trophy at City, made nine changes to the side that throttled Real Madrid in their Champions League semi-final, second leg on Wednesday.
"I can't actually speak highly enough of the manager," Grealish said. "Listen, he's a bit weird the way he sort of knows everything, some games I'm thinking: what's he going to come up with today? And he comes up with different tactics every game. It's a pleasure to work with him. I love him."
Despite wholesales changes to the team, City still dominated against Chelsea, proving they are a well-oiled machine no matter which parts their mastermind manager has to work with.
City were crowned champions for the third season in a row and fifth in six years a day earlier than expected when Arsenal's 1-0 defeat at Forest doused any remaining hope the Londoners had of catching them.
The mood on Sunday was festive. Chelsea sportingly gave the City players, who had watched the Arsenal game together the previous evening, a guard of honour before kickoff while thousands of fans rushed onto the field after the final whistle.
Rather than spending a few minutes to soak up the atmosphere, the players were quickly shepherded down the tunnel by security.
Despite announcements to leave the pitch immediately, nobody was in a hurry and the mass of sky blue fans lit flares and pulled at the goalposts. One supporter hoisted a banner that read "The Treble is On."
Guardiola led the players out for the trophy celebration, high-fiving each member of the team staff on the way. Haaland received the loudest cheer while his smiling dad Alfie, who once played for City himself, filmed with his mobile phone.
Haaland had been a late substitute and did not extend his record of 36 goals in a single Premier League season.
"I don't know what to say, I didn't plan to say anything," Norway striker Haaland said. "I feel a special connection with the fans... 36 goals, Premier League trophy, debut season, two finals left, not a bad start."
Raheem Sterling nearly equalised in the second half but defender John Stones made a spectacular sliding stop after the ex-City forward beat keeper Stefan Ortega.
Stones wrapped a friendly arm around fellow England international Sterling after his near-miss, while City fans saluted their former player with a standing ovation when he was substituted.
They could afford to be generous with their team basking in the glory of another domestic title triumph.