Even though the defeat means Lazio are just five points above the drop zone with two games to go, their supporters were glad bitter city rivals AS Roma have slipped back to second spot.
Lazio coach Edy Reja was adamant his side would try to win the game but Jose Mourinho's Inter produced a fine display to move two points clear of Roma, who beat Parma 2-1 on Saturday.
Defender Walter Samuel found the breakthrough on the stroke of half time when he expertly headed in Wesley Sneijder's cross to prompt cheers of joy throughout the Stadio Olimpico.
Thiago Motta then nodded in a corner in the second half to keep Inter on course for an unprecedented Italian treble ahead of Wednesday's Cup final with Roma and the Champions League final on May 22.
"Two games remain and it will be tough but we've taken an important step," the Brazilian told Sky TV, aware his side can win their fifth straight scudetto at home to Chievo next weekend if results go their way.
Juventus earlier suffered the latest and biggest embarrassment of a terrible season when their slim Champions League hopes were extinguished in a 1-1 draw at Catania.
The twice European champions, Serie A's most successful club, have lurched from one bad result to another this term and respite from the misery never looked likely in Sicily despite Claudio Marchisio equalising Matias Silvestre's opener.
Beleaguered Juve lie seventh, assured of a Europa League qualifying berth next term like sixth-placed Napoli but eight points behind fourth-placed Sampdoria with two matches left.
SIENA RELEGATED
Samp stayed two points clear in that final Champions League qualifying spot thanks to a 2-0 home win over relegated Livorno with Antonio Cassano scoring a typically classy goal on five minutes and Reto Ziegler blasting in a late free kick.
Luigi Del Neri's side are four behind third-placed AC Milan after the Rossoneri beat Fiorentina 1-0 on Saturday.
Fifth-placed Palermo are now the only team that can catch Sampdoria and they host them next weekend in a cracking clash.
Strikers Edinson Cavani and Fabrizio Miccoli netted as Palermo won 2-1 at Siena to confirm the home side's relegation after they were effectively condemned last weekend because of their poor goal difference.
Third-from-bottom Atalanta, who missed a first-half penalty and were reduced to 10 men for the second period, stay five points adrift of safety after a calamitous late own goal from Federico Peluso in a 1-1 draw with fourth-from-bottom Bologna.
Peluso sank to his knees and held his head in his hands after he miscontrolled the ball and it ran into the net.
Conceding the freak equaliser followed a strange episode on halftime when the referee awarded Bologna a penalty and dismissed Maximiliano Pellegrino for protesting, then reversed the penalty decision because the ball had been out of play.
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