After being left stunned by Sofiane Feghouli's first-half penalty, Belgium coach Marc Wilmots made two tactical changes that paid dividends as substitutes Marouane Fellaini and Dries Mertens both found the net to secure victory in Belo Horizonte on Tuesday.
Having missed the past two global showpieces, Belgium were caught flat-footed as Feghouli gave Algeria a surprise 25th-minute lead.
The 24-year-old was hauled down by Jan Vertonghen as they stretched for a left-wing cross and Feghouli punished him by sending Thibaut Courtois the wrong way with his spot-kick.
Belgium applied plenty of pressure and eventually got themselves back in the game as Fellaini levelled with a perfectly-placed header in the 70th minute.
Victory was assured with 10 minutes to play when Mertens capped a flowing move, the Napoli midfielder lashing the ball past Rais M'Bolhi.
A cautious start from both sides saw the game bereft of early chances, with Belgium dominating possession and Algeria restricted to breaks on the counter attack.
M'Bolhi was the first to be forced to make a save in the 21st minute as Belgian playmaker Axel Witsel unleashed a powerful strike from 20 yards, but the goalkeeper was equal to it and made a good stop.
Three minutes later, Algeria were gifted the lead as Faouzi Ghoulam raced down the left-hand side unopposed and delivered a perfect cross to the back post that Feghouli looked to get onto.
However, Vertonghen pulled him back inside the penalty area as the Valencia winger stretched every sinew to reach the ball.
Referee Marco Rodriguez had no hesitation in pointing to the spot, with the Tottenham defender booked for his crude tackle.
And Feghouli duly rolled the ball calmly into the back of the net.
Belgium resumed their control of possession after the goal and Witsel tested M'Bolhi again with 10 minutes of the half remaining, but the 28-year-old was able to parry the shot away.
Wilmots introduced Mertens at half-time in an attempt to lift his team going forward, and it nearly had an immediate impact as he delivered a corner that Witsel headed over at the back post.
Eventually Belgium's pressure forced a leveller, though, as Wilmots' third sub, Fellaini, restored parity with 20 minutes remaining.
Kevin De Bruyne, who had been very quiet up to that point, found room on the left and whipped in a cross to the near post for the Manchester United midfielder.
Fellaini was able to get himself in front of his marker and sent a flicked header crashing off the crossbar and into the back of the net.
Mertens then ensured Wilmots will be lauded as a tactical genius in the 80th minute after a lightning-quick break from Eden Hazard led to the winner.
The Chelsea man drew two defenders before finding his team-mate and Mertens made no mistake.
