Yann Bissek's first goal in Italy just before half-time at the San Siro and a late finish from Nicolo Barella were enough for Inter to bounce back from cup defeat to Bologna midweek and keep closest challengers Juventus at bay.
"We came into the game off the back of a result which made us unhappy because we played well in the cup. It was important to win and that wasn't guaranteed after Wednesday's game, so I'm really happy," said Inzaghi.
The 23-year-old Bissek has had a bumpy start to life at Inter but his header from Hakan Calhanoglu's pinpoint free-kick capped a fine performance at centre-back and sent Inter on the way to a fourth straight league win.
Inter are hunting a 20th league title and look in good shape to do that after beating 12th-placed Lecce without injured star striker Lautaro Martinez.
Marko Arnautovic's underwhelming display up front highlighted how much Inter's attack relies on 17-goal Martinez, and their unusual impotency allowed Lecce to stay in the game until Barella doubled the hosts' lead in the 78th minute.
Arnautovic was surrounded by teammates following that strike as it was his deft flick that sent Barella clean through to net his second of the season and end the match as a contest.
"They know I am in a difficult spell," said Arnautovic, who also missed a couple of decent opportunities. I am close to getting back to my best. They can see it, they talk to me every day, but it's not been easy."
Napoli fell a whopping 17 points behind Inter after the latest defeat of a disastrous season as Roma reignited their bid for a top four spot.
Substitute Lorenzo Pellegrini lashed in the opener in 76th minute of a ill-tempered, scrappy encounter at the Stadio Olimpico - which featured 13 bookings and two red
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