However, Belgium improved after the introduction of Marouane Fellaini, and after the Manchester United midfielder had headed in an equaliser, Dries Mertens netted the winner 10 minutes from time to earn his team three valuable points.
Below, Sports Mole assesses whether Belgium were deserving of them.
On target: 8
On target: 1
Was the result fair?
Over the course of the 90 minutes, it's difficult to argue that Belgium didn't deserve to win the match, but they were made to work hard to earn the three points. They have been tipped to go far in this competition, but they offered little in Algeria's half during the first 45 minutes, and they were made to pay when Feghouli gave his team the lead from the penalty spot. However, the introduction of Mertens and Fellaini changed the course of the game, and after Fellaini marked his appearance with a fantastic header from 12 yards, Mertens followed suit with a fine finish after collecting Eden Hazard's pass.
Wilmots had cause for concern after witnessing his team's display during the first half, but the coach will sleep easier after seeing his side turn things around in the second half. Belgium began the match like they were expecting to ease past their opponents, but once it became apparent that Algeria were no pushovers, they struggled to change gears. The improvement finally came in the second half, though, and Mertens, Fellaini and Divork Origi have all staked their claim for a starting spot against Russia at the weekend.
Despite coming into the game as the underdogs, Algeria started strongly and more than matched Belgium during the opening exchanges. Their opening goal was gifted to them by Jan Vertonghen, but it was deserved as they found a way to nullify their opposition's attack. However, Algeria's downfall came after they sat back on their slender advantage, and once Belgium equalised, they soon came under pressure to hold on to a point. They largely tried to keep men back, but on the one occasion when they pushed men forward, Belgium broke clear to score their second, and it ultimately cost them the match.
Sports Mole's man of the match
Marouane Fellaini: Manchester United supporters who never saw the match might think that their eyes are deceiving them, but they are not. After being introduced as a 65th-minute substitute, Fellaini kick-started Belgium's efforts with a superb glancing header from 12 yards and his overall performance saw him trouble the Algeria defence every time that a ball was launched into the area. He has deservedly had his critics throughout the season, but this was the night where Fellaini showed one of the reasons why Manchester United and David Moyes paid £27m for his signature last summer.
While his versatility gives his side more options, Vertonghen looked out of place at left-back and it came as no surprise when he was caught on his heels when a ball was sent into the penalty area, resulting in him hauling down Feghouli. The Tottenham Hotspur defender recovered during the second half, but his mistake almost cost his side the chance to start their campaign with a win.
It's often said that all a referee can do is go about his business unnoticed, and that is what Marco Rodriguez did during this game. The Mexican official had little to do, but when he was called upon, he got every important decision correct. The 40-year-old could have put himself in contention for a role later in the tournament.
Belgium: Belgium face fellow European outfit Russia on Sunday afternoon knowing that a win will almost certainly secure their place in the last 16.
Algeria: Algeria go up against South Korea in their next fixture on Sunday evening with anything but a win seeing their participation in the tournament put under threat.