The host nation were staring at elimination until Hamza Mathlouthi was controversially deemed to have fouled Ivan Bolado in the penalty area deep into second-half stoppage time.
Javier Balboa stepped up and converted the spot-kick, cancelling out Ahmed Akaichi's 70th-minute opener, before Balboa found the back of the net with a stunning 25-yard free-kick 12 minutes into the additional 30.
"Tunisia played very well. They have players who play at a high level, while we only have one who plays in a top division in Europe, and that's Javier Balboa," Becker said afterwards.
"To beat Tunisia is an achievement, almost a miracle.
"Thanks to the players, the people of [Equatorial] Guinea, the people at the federation, their president and of course the president of the Republic."
Tunisia coach Georges Leekens was scathing of the referee following the match as his side crashed out of the tournament.
"In my 15 years as a player and 30 as coach I've never seen anything like it," Leekens told reporters.
"Today's result was forced. The referee made a huge error and we did not deserve that."
And Becker admitted he could understand his counterpart's frustration, having bowed out in such circumstances.
"I understand the Tunisians' anger at having lost, because they had the potential to win by several goals," he added.
"But they didn't do it and in the end the game went our way.
"Everyone will contest a penalty that goes against them. In the last minute, who would not protest? I would have protested too.
"But you still need to score the penalty and luckily we have a specialist in Javier Balboa.
"If we spent all our time scrutinising refereeing, we wouldn't be able to play football anymore.
"It was the team ranked 30th [Tunisia are 22nd] in the world against the 118th, and they couldn't beat us in 120 minutes.
"At the moment I am the happiest man in the world."
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