The Tuscan side headed to Sardinia third from bottom in the standings and seven points behind their hosts, but took control of the game courtesy of Emerson's opener and a Paulinho penalty either side of the break.
Nene pulled one back for Cagliari after 64 minutes, but their hopes of equalising suffered a blow seven minutes later when Daniele Conti saw red for foul and abusive language.
The visitors finished the match even further reduced in numbers following the late dismissals of Federico Ceccherini and Marco Benassi, but held on for the three points.
The first real sight of goal at the Stadio Sant'Elia arrived in the 14th minute when Livorno's Andrea Luci produced a dangerous cross from the byline which was almost turned into his own net by Cagliari defender Dario Del Fabro.
Del Fabro was somewhat fortunate again six minutes later again when some sloppy defending gifted possession to Paulinho, but he over-hit his pass to an unmarked Innocent Emeghara and the chance was gone.
Cagliari were being restricted to long-distance efforts, rarely troubling Livorno goalkeeper Francesco Bardi. Daniele Conti's 25-yard free-kick was too high and Andrea Cossu lashed over the bar as well before Bardi was called upon to keep out a decent effort from Nene three minutes before half-time.
The deadlock was broken by Livorno, though, a minute before the interval, when Emerson's vicious drive from 35 yards flew into the bottom-right corner with Vlada Avramov well beaten.
The Amaranto doubled their advantage eight minutes into the second period. Paulinho got up to take the penalty himself after being brought down by Avramov, who got a touch to the spot-kick but was unable to prevent it crossing the line.
Nene halved the deficit soon after the hour mark with a curling shot following a counter-attack, before Conti's frustrations got the better of him and he was sent off for dissent.
Livorno passed up a great opportunity to wrap up the win 13 minutes from time when substitute Ishak Belfodil failed to find the target with a simple close-range header from a corner.
Ceccherini was sent off five minutes from time, tugging the shirt of Albin Ekdal deemed a second bookable offence, and Benassi followed in stoppage time for a professional foul on Mauricio Pinilla.
Pinilla nearly made the most of the 10-versus-nine situation in the dying moments, but his right-footed shot drifted inches wide of the left post.