Having been drawn against defending champions the USA first up, Igor Kozakovi's men wanted to get their campaign up and running today at Earls Court.
After easing into a 2-0 lead they let their African opponents back in, before closing the match out with ease in the fourth set.
The final tally was 25-15, 25-21, 20-25, 25-18.
Aleksandar Atanasijevic, who is over 2m tall, topped their scoring charts with 24 points - 19 of them on the spike - while Uros Kovacevic chipped in with 19 and Marko Podrascanin blocked eight times.
Hamza Nagga took 22 points away for Tunisia, but their inability to win points on their serve cost them. They had just three unreturned, while Serbia recorded nine.
The Europeans are next up against Germany while still-to-win Tunisia take on Russia.
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