Germany made a remarkable comeback to beat defending champions Belgium 5-4 in the sudden death shoot-out after playing a 3-3 in the regulation time.
With around 60 per cent ball possession, the home side had 14 shots at goal as against nine by South Africa.
Belgium beat the last two editions' runners-up Netherlands in a penalty shootout 3-2.
Abhishek and Harmanpreet Singh scored a brace each at the Birsa Munda Hockey Stadium.
PR Sreejesh suffered an injury in the shootout that the hosts lost 4-5.
India took a 2-0 lead through goals from Shamsher Singh (21st) and Akashdeep Singh (32nd) before Wales stunned the home team with twin strikes in a span of two minutes.
The hosts had earlier started their campaign with a 2-0 victory over Spain.
A win against England, ranked fifth in the world, on Sunday will help India put one foot in the quarterfinals of the World Cup.
Amit Rohidas and Hardik Singh scored as the hosts won 2-0.
The veteran goalkeeper will be playing in his fourth World Cup and third at home.