Livorno took the lead three times, but were pegged back each time by a courageous Catania, who almost snatched victory in stoppage time.
Innocent Emeghara scored two for Livorno and earned a penalty, which was converted by Paulinho.
Gonzalo Bergessio, Pablo Barrientos and Sergio Almiron replied for the hosts, earning them a point which does not help either side much in their respective battles against the drop.
It was the anticipated relegation battle at the Stadio Massimino, and neither side were going to hold back.
The visitors started with even less fear with Emerson and Paulinho both testing Alberto Frison in the Catania goal.
Midway through the half, Catania moved up a gear and Francesco Lodi had a shot blocked from outside the area, lifting the home fans who had hardly done much to back their team until then.
The game opened up as a result and Duncan went close again at the other end as Livorno ended the half stronger, upsetting the home fans, who jeered their team off at the interval.
Their anger augmented five minutes into the second half when Emeghara gave Livorno the lead after Emerson's shot was only parried out to him by Frison.
The home fans made their feelings clear when Sebastian Leto was substituted soon after, and the Argentinian did not respond well, kicking the bench several times in anger.
Catania's response was positive, however, and they levelled through Bergessio in the 61st minute.
His first effort from Barrientos' cross was saved by Francesco Bardi, but he was quickest to react to bundle the ball over the line from close range.
Their joy lasted only 10 minutes before the referee awarded a penalty for Livorno when Frison appeared to push the ball behind for a corner before Emeghara tumbled over his hand.
Paulinho stepped up to beat Frison and put Livorno in front, much to the anger of Catania coach Rolando Maran, whose continued protests against the penalty saw him dismissed.
Catania responded immediately with Barrientos levelling again after being left totally alone in the centre from a corner, which he tapped through the legs of Bardi from five yards out.
However, Livorno raced back up the other end of the field and regained the advantage for the third time with Frison this time only able to complain about himself as he pushed Duncan's shot out to Emeghara, who accepted his second gift of the game.
The game was not over, though, and Catania levelled once again when the Livorno defence again let a player over, this time Almiron, who brought the Sicilians level for the third time in the game.
Francesco Lodi nearly stole all three points for Catania in stoppage time, but Bardi kept the ball out in a frenetic ending.