Crotone's win was only their fifth of the season and by far the most impressive scalp for the team from Calabria who are playing in the top flight for the first time.
Roma stayed six points behind Juventus who beat Chievo 2-0 on Saturday. Both teams have seven matches to play, including a meeting at the Stadio Olimpico on May 14.
Napoli strengthened their grip on third place, which earns a place in the Champions League playoff round, with a 3-0 win at fourth-placed Lazio, opening up a seven point gap over their opponents and remaining four behind Roma.
Federico Fazio put Roma ahead from close range in the 26th minute and Mohamed Salah added another before halftime when he latched onto Edin Dzeko's pass and cleverly lobbed the ball over Antonio Mirante.
Dzeko completed the scoring in the 75th minute when he tapped in Diego Perotti's cross for his 24th goal of the season, making him the league's joint topscorer.
Crotone floored Inter with two goals from forward Diego Falcinelli in four minutes midway through the first half.
Falcinelli converted a penalty, awarded for handball by Gary Medel, in the 19th minute and then beat the offside trap to run onto Marcelo Trotta's pass and lob the ball over Samir Handanovic.
Danilo D'Ambrosio pulled one back for Inter in the second half but Crotone held out for an historic win which increased their hopes of pulling off a great escape.
Read the full article on eurosport.co.uk: Roma keep up dogged pursuit of Juventus, Inter stunned