The Argentine stroke home from the spot after Biancocelesti goalkeeper Federico Marchetti had been dismissed for hauling down Mbaye Niang midway through the first half
The Biancocelesti began brightly at the Stadio Olimpico but the entire complexion of the game changed midway through the first half when Federico Marchetti was dismissed for taking down Mbaye Niang in the area.
Diego Perotti stroke home the resulting spot-kick and although 10-man Lazio fought bravely to try to salvage a point, with Stefano Mauri striking a post in the second half, Genoa held on to end a run of seven games without a win and move to seventh in the table, just two points behind their hosts.
Lazio had been heavy favourites to prevail and Stefano Pioli's men made a stirring start, striking the woodwork just seven minutes in.
Lucas Biglia must have thought he had scored with a fine free kick from just outside the area but Mattia Perin got down wonderfully well to his right to push the ball away to safety with the aid of the base of the post.
The hosts threatened again seconds later but again Perin came to the Rossoblu's rescue, pulling off a terrific one-handed stop to keep out Antonio Candreva's fierce near-post drive.
Genoa gradually grew into the game, though, with Niang causing problems with his pace and fancy footwork.
Indeed, the on-loan AC Milan striker had already called Marchetti into action with a decent free kick when he expertly controlled a long ball over the top from Andrea Bertolacci 28 minutes in before touching it past the onrushing Lazio shot-stopper.
Marchetti clattered into Niang and even though Stefan de Vrij had raced back to cover, referee Andrea Gervasoni had no hesitation in issuing a red card.
Pioli sent Etrit Berisha on in place of Danilo Cataldi but the reserve goalkeeper was completely bamboozled by Perotti's incredibly cool penalty, with the Argentine calmly strolling up to the ball before nonchalantly rolling it into the right corner.
With a man advantage, Genoa unsurprisingly dominated possession thereafter but they squandered a succession of chances to kill the game off.
Iago Falque was the principal culprit, with the Spaniard firing wastefully wide just after half-tme after being put clean through on goal by the impressive Niang.
Falque found himself one on one with Berisha again midway through he second half but he fired straight at the Lazio replacement.
His profligacy was very nearly punished too, with Mauri winning the race to a Miroslav Klose knockdown only to then see his low strike come back off the right post.
As it was, though, Genoa survived late Lazio pressure to register their first Serie A win since beating AC Milan at the Luigi Ferraris on December 9 - yet their eighth in a row over the Biancocelesti.