The outlook was bleak for the Clarets even prior to kick-off, having conceded 32 consecutive goals without mustering a reply against City.
Erling Haaland’s long-awaited return from injury therefore came at an ominous time, but Pep Guardiola stuck with Alvarez up top on his 24th birthday, and the Argentine was just as devastating.
Matheus Nunes made City’s opener, directing a pinpoint cross for Alvarez to head home from the edge of the six-yard box, before a quick-thinking set-piece routine caught the visitors off guard.
Kevin De Bruyne was the architect, playing his free-kick along the ground as a through-ball for Alvarez, who bagged his second of the night with a clinical finish past James Trafford.
It wasn’t a half devoid of all opportunity for Burnley, as Lyle Foster finally gave the travelling fans something to think about minutes before the interval by cutting in from the left and curling an effort past the far post, but Vincent Kompany trudged back to the dressing room knowing his side were fighting an uphill battle.
The gradient got steeper just 27 seconds after the restart, when Phil Foden rolled a tempting ball across the edge of the box for Rodri to slot home and rubber-stamp the result.
The Clarets kept plugging away as City engaged cruise control, but it took until stoppage time to notch their first goal in nine games against the Sky Blues, with David Datro Fofana’s fine run and low cross turned in by Ameen Al-Dakhil.
Burnley are now five games without a win and seven points from safety, as Kompany gears up for a tough triple-header against Fulham, Liverpool and Arsenal.
City, meanwhile, will fancy their chances of keeping the pressure on their title rivals by banking maximum spoils from upcoming games against bottom-half duo Brentford and Everton.
Flashscore Man of the Match: Julian Alvarez (Manchester City)
