Milan Skriniar and Ivan Perisic were on target for Inter, who finished seventh last season, as Luciano Spalletti's side survived a hard second half to make it four wins out of four.
Luciano Spalletti warns having no European commitments "can be an advantage or an extra difficulty" for Inter as they visit Crotone.
But Spalletti's side suffered in the heat until late strikes from Milan Skriniar and Ivan Perisic secured the three points.
Bruno Martella went close from a free-kick after Miranda was booked for clumsy challenge, slamming the ball just wide of Handanovic's right post.
Crotone's picked up the momentum after the break and should have been ahead five minutes into the period with Tonev again involved as he latched onto a long ball over the top of the Inter defence but shot straight into the path of the Slovenian keeper.
Davide Nicola's plucky hosts continued to hold their own but their resistance was finally broken in the 82nd minute when Skriniar, a summer signing from Sampdoria, notched his first goal for his new club.
"It was not easy and our players were very professional, adapting to a style of game they were unaccustomed to", Spalletti told Mediaset Premium. We put faith in him and he's a tough starter for those who show faith.
Inter Milan's Ivan Perisic celebrates scoring their second goal with teammates during the Serie A match between FC Crotone and Inter Milan, at Stadion Ezio Scida, in Crotone, Italy, on September 16, 2017.
Crotone, who pulled off one of the greatest escapes in Serie A history to avoid the drop last term, have one point and look to be in for another hard season.
Edin Dzeko, who made headlines for criticising di Francesco's tactics in the Atletico stalemate, hit back with a brace on 34 and 61 minutes and Alessandro Florenzi marked his comeback after almost a year out injured with an assist.
Roma, last season's runners-up, have six points but have played only three games. In the previous four, it finished in the top four at the end of the season. Verona, who had Samuel Souprayen sent off in the 66th minute, have one point.
Bologna stifled the hosts' attack in the first half before Federico Chiesa broke through on 51 minutes with a curling shot into goal only for Rodrigo Palacio to equalise a minute later.
Inter are now top of the Serie A table, with title rivals Juventus and Napoli playing on Sunday.