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Sunelita finally broke the deadlock in the 47th minute to seal the issue.
This will be the team's first outing under new chief coach Craig Fulton.
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.
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.
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.
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.
Defender Amit Rohidas has been named Harmanpreet's deputy.
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