Fellaini was on the scoresheet as Marc Wilmots' men began their Group H campaign with a 2-1 victory over Algeria.
That triumph has further raised hopes of Belgium, considered darkhorses before the tournament began, going on to lift the trophy.
Fellaini certainly believes that is possible, saying: "Belgium are capable of winning the World Cup. If that proves the case I promise that I will shave my hair."
The midfielder also claimed he did not enter the showpiece with an extra point to prove despite a poor first season with Manchester United.
"For me the match was not a case of answering my critics," he added. "I don't owe anybody anything.
"My goal is to score for the team for my family and for the country. I had a difficult season but now I am at the World Cup and I am focussed on the national team."
