It was a well-deserved first win for new head coach Davide Ballardini, whose side built a two-goal lead inside 21 minutes thanks to goals from Marco Borriello and Andrea Bertolacci.
But the hosts would have to fight to the very end for the three points as Sergio Floccari and Stefano Mauri dragged Lazio back into the game, only for deadline-day signing Rigoni to fire Genoa up to 17th place with a bullet header at the death.
Lazio started with a spring in their step but neither Lorik Cana nor Floccari could capitalise on defence-splitting passes from Cristian Ledesma before Genoa took an early lead.
Borriello rose highest to meet an inswinging corner in the 16th minute, nodding the hosts ahead and igniting the game as a contest.
That spurred the Rossoblu on to greater things and, after Marco Rossi was flagged for offside when through on goal, they doubled their lead in the 21st minute.
With Lazio struggling to organise their lines, Bertolacci found the space he needed to steer a left-footed drive beyond a stranded Federico Marchetti.
The visitors could barely get a touch of the ball and Marchetti was soon forced to cut out a tricky one-two between Bertolacci and Emiliano Moretti.
Alvaro Gonzalez came closest to reducing the arrears before the break, connecting well with Ledesma's dipping free-kick but scooping the ball over the bar.
Borriello showed tremendous athleticism to get within scoring range 10 minutes into the second half but his final touch was wayward.
And with that opportunity to make it 3-0 passing Genoa by, Lazio duly halved the deficit in the 58th minute.
Floccari had been a largely isolated figure in attack but he made the most of a rare Lazio raid forward, twisting his body to slam the ball home off the underside of the crossbar.
Despite their early dominance, Genoa appeared rattled by the Biancocelesti response and only a lack of accuracy from Abdoulay Konko kept the visitors from equalising in the 75th minute.
Borriello had been the architect of much of his side's best football but he allowed Lazio back into the game with eight minutes remaining.
The former Juventus man was penalised for handling the ball during a tussle with Cana and Mauri stepped up to convert the resulting penalty.
However, Genoa would have the final word as substitute Rigoni appeared in the right place five minutes into stoppage time to head home an invaluable winner.