City entered the game on a 26-match unbeaten run at home in the Champions League, and normal business was resumed almost immediately after the restart when lvarez levelled after combining with Erling Haaland.
On the hour, a mistake by Red Star keeper Omri Glazer enabled a lvarez cross to go in, and Rodri made it 3-1 with a clinical goal after 73 minutes as City made it 19 home wins in a row in all competitions.
After finally claiming Europe’s biggest club title with a triumph over Inter Milan in Istanbul just over three months ago, City began their defence in ultimately easy way.
But for 45 minutes, it appeared to be one of those nights, as chance after chance went begging.
When Argentina’s Alvarez equalized in the 47th minute, only one outcome seemed likely.
Norwegian goal-scoring machine Haaland has now gone four Champions League games without scoring, and he was responsible for several terrible misses in a first half in which City had the most goal attempts in the league since data collection began.
He headed one effort wide, missed another easy chance against the crossbar, and then fired over.
In the first half, Red Star keeper Glazer was outstanding, rejecting Phil Foden from close range as well as Nathan Aké and Rodri.
But, in the 45th minute, City became silent, and a throw forward put Bukari through with only Éderson to beat.
The Ghanaian blasted past the City keeper with remarkable coolness, but his celebration was cut short by an offside flag before referee Joao Pinheiro allowed it to stand following VAR intervention.
The 3,000 Belgrade fans celebrated, and City couldn’t believe it as they left at halftime.
After the break, though, City quickly made amends as Alvarez fed the ball into Haaland and then showed great intent to dash into the area and grab a return pass before skipping by Glazer and slotting home in the blink of an eye.
Kyle Walker had a goal disallowed for offside before Glazer gifted the hosts their second goal.
Glazer flapped at thin air as Alvarez blasted in a right-footed cross that nestled in the net.
Rodri, who scored the winner against Inter in June, struck a lethal right-foot strike from the left side of the penalty box as City began to toy with a flagging Red Star.
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