Treble-chasing City, who wrapped up the title when second-placed Arsenal were beaten at Nottingham Forest yesterday, have won 12 successive games in the top flight.
They 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.
Reuters reports 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 today and two huge games on the horizon - the FA Cup and Champions League finals - City manager Pep Guardiola left his big guns, including goal-scoring machine Erling 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.
City still dominated, proving they are a well-oiled machine no matter which parts the mastermind manager has to work with.
"It was a great feeling," midfielder Kalvin Phillips told Sky Sports after making his first Premier League start for City. "I was happy because we won the league and I knew there might be a chance I could play. I have enjoyed every moment.
"It has been unbelievably tough this season and probably the lowest point confidence-wise in my career."
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 today 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 by security down the tunnel.
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 fan hoisted a banner that read "The Treble is On."
Haaland was a late substitute and did not extend his record of 36 goals in a single Premier League season.
Raheem Sterling nearly equalised in the second half but John Stones made a spectacular sliding save after the ex-City forward beat keeper Stefan Ortega.
Stones wrapped a friendly arm around Sterling after his near-miss, while City fans saluted their former player with a standing ovation when he was substituted.
Erling Haaland with the Premier League trophy Photo: AFP