The home side dominated possession, but for much of the encounter they barely tested Tunisia's keeper and had only a few tame shots and a couple of missed half-chances even after the visitors had a man sent off with almost half an hour to play.
Only in the 89th minute did substitute Nacer Chadli find Mertens in space in the penalty area and he calmly stroked it in with his right foot.
One note of concern was that striker Romelu Lukaku, who only came on for the last half hour, hobbled off in injury time.
"Romelu has difficulty walking. It's a big bruise. I think it'll be three or four days. We'll do some additional tests tomorrow," Belgium coach Marc Wilmots said.
Belgium, with a loss and a draw against Tunisia from their two previous matches, chose to rest regular midfielders Kevin De Bruyne and Axel Witsel and, for most of the match, Lukaku.
Until the goal, the highlight of a tight contest was arguably a fierce hailstorm midway through the first half with hailstones as large as golf balls battering the pitch, forcing a 45-minute pause.
After play resumed, both 19-year-old striker Divock Origi and Kevin Mirallas were put through, but failed to find the target.
Tunisia, managed by Belgium coach Wilmots's predecessor Georges Leekens, had tight defensive and deep midfield lines with only one man up front.
When Tunisia's Issam Jemaa was sent off for a second yellow card in the 64th minute, they played without an obvious striker, and withstood wave after wave of Belgian attacks.
"It was the first time playing against a five-man defence. It was like a wall in front of us," Wilmots said, adding it was unlikely to be repeated at the World Cup and that first opponents Algeria pose a greater attacking threat.
Tunisia, who lost a World Cup qualifying playoff to Cameroon, had beaten World Cup finalists South Korea in Seoul 10 days earlier.
Coach Leekens was reluctant to be drawn on Belgium's chances. "I'm also a proud Belgian and we have a good team but I won't say how far they'll get. I think it's best to avoid Germany in the second round," he said.
Belgium fly to Sao Paolo on Tuesday, with a practice match behind closed doors against the United States pencilled in for Thursday. Belgium face Algeria in Belo Horizonte on June 17, with Russia and South Korea their other group H opponents.


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