Second-half goals from substitutes Marouane Fellaini and Dries Mertens secured an opening Group H victory for the Red Devils after Algeria had taken a 25th-minute lead via a Sofiane Feghouli penalty after he had been hauled down by Jan Vertonghen.
But Fellaini, who endured a miserable, goalless season with Manchester United, levelled with a powerful header in the 70th minute.
Ten minutes later, Mertens buried the second goal to give Belgium a winning start in a Group H which also includes Russia and South Korea.
Algeria stunned the fancied Belgians after Tottenham’s Jan Vertonghen wrestled livewire Valencia striker Sofiane Feghouli to the ground.
Vertonghen was yellow-carded while Feghouli held his nerve to tuck a confident penalty beyond Thibaut Courtois in the Belgium goal.
It was Algeria’s first World Cup goal since 1986 and conjured up memories of their famous 1982 win over West Germany.
Belgium were poor in the first half and had to wait until the end of the first half for their first serious attempt on goal when Nacer Chadli was put clean through by Eden Hazard.
But Chadli’s effort was well-saved by Rais M’bolhi.
Belgium coach Marc Wilmots, who has never lost a competitive fixture as national team coach, took off the sluggish Romelu Lukaku.
On came Divock Origi and then Fellaini and the more muscular approach paid off.
Fellaini headed in a pinpoint cross from Kevin De Bruyne’s and 10 minutes later it was 2-1 as Mertens was left in too much space by the tiring Algerians and the Napoli man drove the ball home.
Another Fellaini header was tipped over by M’bolhi as Belgium finished the strongest before a quick breakaway involving Origi and Eden Hazard released Mertens to fire in the winner with ten minutes to go.