Belgium, who were without Eden Hazard and Romelu Lukaku and only brought on Kevin De Bruyne in the second half, hit the woodwork three times.
Chelsea beat Aston Villa 3-0 for their 600th Premier League victory to move joint top of the standings alongside Manchester United.
Lukaku needed only 15 minutes to get off the mark for the Blues after his reported 97.5 million pounds transfer from Inter Milan.
The Belgium international is in line to feature against Arsenal in the Premier League on Sunday.
A Chelsea statement did not mention the agreed transfer fee, but media reports say the deal is worth a club record 97.5 million pounds ($134.7 million).
Belgium were among the favourites for the tournament, having spent more than 1,000 days at the head of the FIFA rankings.
The Belgians, top of the FIFA rankings, went ahead after only 10 minutes through Lukaku.
Sevilla scored a roller-coaster 3-2 win over Inter Milan after an overhead kick by defender Diego Carlos deflected by the Italian side's top scorer Romelu Lukaku settled a gripping final.
United were forced to dig deep as Portuguese midfielder Bruno Fernandes converted a 95th-minute penalty to secure a 1-0 win over FC Copenhagen after extra time.
Inter posted a photograph of the Belgian forward wearing the shirt on the club's Instagram account one day after confirming that they had signed him from Manchester United.