The Red Dragons found themselves a goal down after 24 minutes at the Estadio Mineirao, before hitting back with two goals in the final 20 minutes to edge past a tiring Algerian side.
"It was a tough match but we were patient throughout and at the end we were rewarded," Wilmots is quoted as saying by BBC Sport.
"We stayed calm after doing a small mistake in the first half. We got a new momentum. We saw that Algeria were getting more and more tired.
"At half time people were a bit down, but I said 'don't worry, we will score and we will change totally the match'."
Belgium return to action on Sunday when they take on Russia.