Alessandro Bastoni's first Inter goal was not enough to see off Lecce, who battled to a draw, ending their four-match losing run in Serie A.
Inter were held for the second consecutive Serie A match as a 1-1 draw at Lecce handed reigning champions Juventus an unexpected boost in the title race.
Antonio Conte's men started 2020 with an impressive defeat of Napoli, but they only took a point against Atalanta last week and again failed to register a victory on Sunday.
It had briefly appeared as though 20-year-old defender Alessandro Bastoni would prove the unlikely hero when he headed in the opener - his first goal for the club - three minutes after arriving from the bench.