Midfielder Medel, who joined Inter from Cardiff at the start of last season, drove a long-range shot past on-loan Arsenal keeper Wojciech Szczesny.
Roma dominated the second half but could not find a way past Inter goalkeeper Samir Handanovic as they lost for the second time this season.

The visitors finished with 10 men after midfielder Miralem Pjanic was sent off.
Pjanic was booked just before half time and received a second yellow card for handball in the 72nd-minute as Roma's five-match winning run in the league came to an end.


Inter Milan's players celebrate going top of the table
Inter Milan last won the Serie A title in 2010
Pjanic had earlier been close to an equaliser as Roma battled to recover from Medel's 31st-minute strike but his shot was saved by Handanovic, who then blocked the follow-up from former Chelsea winger Mohamed Salah.

Handanovic also twice kept out headers from former Manchester City forward Edin Dzeko, who was slow to react to a chance to give Roma a first-half lead after a Maicon shot had also been saved.
Medel said: "I'm happy for the fans and my team-mates. I'm delighted with my goal and our win.
"We knew this was a massive game and a chance for us to overtake them at the top."
Napoli will replace Inter at the top of the table if they win at Genoa on Sunday.