After a goalless first half, Napoli forward Dries Mertens opened the scoring for Belgium with a spectacular long-range volley soon after the restart.
Manchester United striker Romelu Lukaku added a diving header from Kevin De Bruyne's cross in the 69th minute to extend his scoring record for Belgium to 37 goals.
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The 25-year-old netted his second of the night, clinically finishing off Eden Hazard's pass, just six minutes later.
Belgium, who reached the quarter-finals at the previous tournament in Brazil, will next take on Tunisia in Moscow on Saturday while Panama will face another tough challenge in the form of England in Nizhny Novgorod on Sunday.