The victory lifts the defending champions to seven points behind leaders AC Milan, who drew 0-0 with Lazio on Tuesday, while a game in hand for Leonardo's third-placed side makes the scudetto run-in even more interesting.
Inter's bid for a sixth straight title was floundering under Rafael Benitez, who left in December after six months in charge, but ex-Milan boss Leonardo has quickly rediscovered the spark which took them to a Jose Mourinho-inspired treble last term.
Kharja, signed on loan from Genoa last week to boost Inter's injured ranks, broke the deadlock on 70 minutes when he finished off some good interplay with Samuel Eto'o.
Giampaolo Pazzini then netted his third goal in two games for his new club on the counter-attack deep into stoppage time before substitute Wesley Sneijder marked his return from over a month out injured with the final goal.
"Tonight it was difficult to find space. We faced a Bari side who are bottom in name only," Leonardo told Sky TV.
"There are still lots of games left and even if we don't forget we have won six of the last seven in the league, it doesn't count for anything now, only at the end."
The score slightly flattered Inter, whose three-pronged attack with goalpoacher Pazzini out wide looked disjointed before Dutch playmaker Sneijder's introduction.
They were also fortunate not to concede in the first half and they could have be down to 10 men before Kharja's opener after the officials missed left-back Cristian Chivu lashing out at defender Marco Rossi.
"We have talked about it. A wrong thing is a wrong thing. It's an internal issue and we'll deal with it," Leonardo added.
Post-match television evidence will probably lead to a ban for Chivu and could give Inter's new Japan left-back Yuto Nagatomo the chance to make his debut in Sunday's big league clash at home to last season's runners-up AS Roma.
Bari, who stayed up easily last term in their first season back thanks to some delightful football, look doomed this time after falling nine points adrift of safety with 15 games left.
