Jorge Costa's men beat 2013 finalists Burkina Faso 2-0 in their tournament opener and would have moved into an unassailable lead at the summit with another three points in Bata.
However, Prince Oniangue capitalised on some questionable Gabon defending to score the winner three minutes after half-time.
Neither side was able to take control in a tight first half, but Frederic Bulot was unlucky not to break the deadlock with a spectacular strike after five minutes.
Oniangue's goal gave Congo something to defend, although Gabon came agonisingly close to finding a leveller when Bulot saw a great chance hit the outside of the right-hand post.
The result sees Congo, who drew 1-1 with hosts Equatorial Guinea in the event's curtain-raiser, go top of Group A ahead of the last round of fixtures.
Both sides made just one change from their opening matches, with Gabon bringing Aaron Ondele in for Yrondu Musavu-King at the back, while Francis N'Ganga made way for Dimitri Magnokele in the Congo XI.
Gabon looked to be full of confidence after kicking off the tournament with a victory, and almost went ahead with a rasping effort in the fifth minute.
A deep cross from the left was met by a neat Malick Evouna flick, but Bulot's rifled shot from the edge of the penalty area was tipped over by Congo goalkeeper Christoffer Mafoumbi.
Congo's Arnold Bouka Moutou lashed a volley into the side-netting at the other end, before Evouna saw his effort trickle wide via a deflection after racing on to a throughball in the 19th minute.
Recent encounters between these sides have been tight affairs - Congo beat Gabon 1-0 at home during qualifying for the 2014 World Cup before a goalless draw in the return fixture - and this meeting was shaping up to be no different.
Levy Madinda had a glorious chance to hand Gabon a half-time lead shortly before the interval, but dragged his shot wide of the left-hand upright after showing great composure in the box, before Pierre-Emerick Aubameyang stung the palms of Mafoumbi from a free-kick.
However, it was Congo who eventually struck first, with Oniangue firing home after defenders Ondele and Bruno Ecuele Manga had got in each other's way while trying to head clear from a corner.
Oniangue went close to doubling his - and Congo's - tally when he unleashed a volley from the edge of the box soon after, but Gabon keeper Didier Ovono punched clear.
Aubameyang headed wide as Gabon chased an equaliser, before Bulot sent a low effort against the post when he should have pulled his side level midway through the second period.
Gabon continued to apply the pressure as the match approached a conclusion, but the Congo back line held firm to leave Claude Le Roy's men a point clear at the summit heading into Sunday's closing group fixture against Burkina Faso.
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