The Belgians, who breezed through the qualifiers unbeaten, have arrived in Brazil as one of the top title favourites with arguably their best team in a generation. (Agencies)
Yet a lackluster first half and a below-par performance by some of their top players, including Eden Hazard and Romelu Lukaku, had them fretting at halftime before a dominant second period that confirmed their status as Group H favourites.
Wilmots has his talented substitutes to thank for the win as Marouane Fellaini and Dries Mertens scored late in the game to turn things around after Algeria's first half lead.
It is that depth of quality that makes Belgium so dangerous with more than 11 players capable of playing top level football.
Belgium had 10 shots on goal compared to Algeria's one as they outclassed their opponents throughout the match but their World Cup opener did give them the jitters initially.
With hugely talented players such as Thomas Vermaelen, Kevin Mirallas, Nicolas Lombaerts and Adnan Januzaj left on the bench, Belgium have lots of firepower in reserve for the coming games.
Not many World Cup teams can boast substitutes of such calibre and then have the luxury of not playing them.
"We have a very good backroom with very good substitutes," Wilmots said.
"I have very powerful players,” he added.
Belgium have a long history in the World Cup and were semi-finalists back in 1986 but the team had not qualified for the tournament since 2002.
There was more good news later on Tuesday with group rivals Russia and South Korea drawing 1-1, leaving Belgium alone at the top of the section.
"We have three points. Now we'll rehydrate, go home and relax. With three points we're nowhere," said Wilmots, who as an attacking midfielder was part of four Belgium World Cup teams.
They next face Russia on Sunday at the Maracana.
The Belgians, who breezed through the qualifiers unbeaten, have arrived in Brazil as one of the top title favourites with arguably their best team in a generation.