Samuel Eto'o tapped Inter ahead on the rebound in the 14th minute after Lazio keeper Fernando Muslera had palmed out a header by the Cameroonian.
Lowly Lazio rallied in sub-zero temperatures at the San Siro but, apart from an appeal for handball against Maicon in the area, they created few clear chances for all their possession.
Champions Inter will go into the winter break with 39 points from 17 matches.
Second-placed AC Milan have 31 points and a game in hand after their visit to Fiorentina on Saturday was one of four weekend fixtures to be postponed due to heavy snow.
AS Roma beat Parma 2-0 to go fourth thanks to second-half goals by Nicolas Burdisso and Matteo Brighi.
Third-placed Juventus, who have 30 points, were sunk by substitute Mariano Izco's late goal after Bosnian midfielder Hasan Salihamidzic had cancelled out Jorge Martinez's 23rd-minute spot kick for Catania.
FERRARA PRESSURE
Defeat piled the pressure on Juve coach Ciro Ferrara after his team also lost 3-1 at Bari last weekend and were knocked out of the Champions League following a 4-1 drubbing by Bayern Munich.
"Our ship is in the middle of a storm and the only way out is staying united," Ferrara was quoted as saying by La Gazzetta dello Sport's website.
"The thought of quitting has not crossed my mind. If there were just one problem we'd have probably solved it.
"There are a series of things that aren't right. We know we haven't done as well in the last three months as at the start of the season but the solution is not in the transfer market," added Ferrara.
Club president Jean Claude Blanc said the former Italy and Juve defender's job was safe. "We have confidence in Ciro and his staff," said Blanc.
The side received a hostile reception from some supporters on Sunday, with several standing with their backs to the pitch during the game. Media reported that racist chants could be heard from the stands.
Sunday's matches between Genoa and Bari, and Udinese and Cagliari were hit by the weather along with Bologna's home game with Atalanta.
