The win moved them up to second but they still trail leaders and city rivals AC Milan by eight points with just four games left.
It has been a largely disappointing season for the team that won everything a year ago, with Rafael Benitez dismissed in December as the team lay eighth and 13 points off top.
Leonardo dragged Inter back into the title race -- they were just two points behind Milan before the derby at the beginning of this month -- but they then fell hopelessly away.
A 3-0 defeat in the derby was followed by a 7-3 aggregate loss to Schalke 04 in the Champions League quarter-finals.
The only saving grace is the 1-0 lead they hold over Roma ahead of the Italian Cup semi-final second-leg in a couple of weeks.
It has got many speculating that Leonardo's time is up amid rumours that treble-winning coach Jose Mourinho will return next season.
"It's not the right time to think about my future, it's been a strange season with our rhythm disrupted many times by injuries and also by the change of coach, but the heart has always been there," he said.
"The foundation of the team is there and will remain, even though we can improve. My behaviour and my relationship with Inter has never changed, it's always the same.
"So I'm not worried, I'm thinking only about finishing the season and achieving our objectives.
"I have a contract with the club and I'm working to attain our goals. I'll go forward with clarity and for the good of Inter. I'm not putting myself ahead of the club and the team."
Midway through the first half on Saturday, the champions found themselves a goal and a man down after goalkeeper Julio Cesar had been sent-off for bringing down Mauro Zarate in the box.
The dismissal seemed harsh given Andrea Ranocchia had got back onto the Inter line as Zarate tried to go around the Brazilian goalkeeper, but the Argentine forward then beat substitute Luca Castellazzi from the spot.
But Wesley Sneijder curled home a delectable free-kick and Samuel Eto'o pounced on a slip from Giuseppe Biava to put the hosts in front.
And when Lazio captain Stefano Mauri was harshly sent off for an innocuous-looking foul on Japanese full-back Yuto Nagatomo, Inter held on comfortably.