Tom Adeyemi hit the post for Leeds, but Ameobi gave the Trotters the lead as he volleyed in Jose Casado's corner.
Bolton were unable to capitalise on their first-half dominance and were punished after Prince Gouano was shown red for fouling Antenucci in the box.
Antenucci fired the penalty beyond Ben Amos, but the hosts held on to deny Steve Evans a first win as Leeds boss.
The result means Bolton remain rooted to the bottom of the Championship table, having now failed to win in seven games.
The Trotters dominated in the opening stages, but almost fell behind as Adeyemi fired Luke Murphy's corner against the woodwork.
Liam Feeney shot narrowly wide for the hosts, who took a well-deserved lead when an unmarked Ameobi powered a volley beyond Marco Silvestri.
Feeney missed a chance to double the lead when he shot straight at Silvestri after being played through by Ameobi, while Leeds striker Chris Wood drew a good save from Ben Amos just before the break.
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Leeds created the better of the chances early in the second half, with Adeyemi unlucky not to equalise when his 20-yard effort was turned onto the post.
United's pressure finally told when Prince tripped Antenucci to stop a quick break, and the Italian sent Amos the wrong way for his first goal in seven games.
But the visitors struggled to test Amos after Prince's sending off, as Leeds' winless run was extended to five games.
Mirco Antenucci's penalty helped Leeds earn a draw at 10-man Bolton, despite Shola Ameobi's debut goal.