The Serie A stalemate will be seen as little help to either club's hopes of gaining a Champions League place for next season, and gives Lazio the chance to take third place when they face second-bottom Pescara on Monday.
AC Milan, for whom Mario Balotelli was a threat in attack, stand third for now, a point ahead of Lazio and Inter but six points adrift of second-placed Napoli.
Stephan El Shaarawy scored the opener for Milan with a dipping left-footed drive in the 21st minute. But substitute Schelotto made an impact off the bench, heading in after 72 minutes to ensure Inter would not finish empty-handed.
Juventus extended their lead at the top of the table to seven points thanks to a 3-0 home win over Siena. Stephan Lichtsteiner scored a 30th-minute opener and Sebastian Giovinco made it 2-0 after 74 minutes, with Paul Pogba then netting a third goal in the dying stages.
Daniele Conti scored the winner deep into stoppage time as Cagliari and nine-man Torino contested one of the most dramatic games of the Serie A season - inside an empty stadium.
Cagliari won it 4-3 but the Sardinian club were barred from hosting fans at the Stadio Is Arenas due to ongoing safety concerns and local supporters were urged to stay at home and follow the game on television.
Marco Sau gave the hosts the lead from the penalty spot during the first half following a careless foul from Angelo Ogbonna. The second half, though, was played at breakneck speed as the lead changed hands three times thanks to quickfire goals between Alessio Cerci, Alen Stefanovic, Conti, Mauricio Pinilla and Rolando Bianchi.
Torino eventually lost both Ogbonna and his defensive replacement Abou Diop to red cards and Conti duly exploited the space to drive in a scintillating winner from long distance, just seconds before the final whistle.
Sampdoria moved clear of opponents Chievo to effectively banish any relegation fears thanks to a 2-0 win at a snowy Stadio Luigi Ferraris in Genoa. Andrea Poli gave the home side the lead in the 33rd minute before the sleet turned to snow, and Eder struck the second with seven minutes remaining.
Catania survived a late onslaught and the dismissal of Nicola Legrottaglie to continue their march towards Europe with a 2-1 victory at Parma.
The Sicilians knew that three points from the Stadio Ennio Tardini would give them a share of sixth place with Fiorentina, whose game at Bologna was postponed, and first-half goals from Francesco Lodi and Keko were enough to see them through.
Parma's Amauri forced a consolation goal with time running out.
Roma defied both the weather and spirited Atalanta resistance to claim back-to-back Serie A victories for the first time in 2013, winning 3-2 away from the capital.
The match at the Stadio Atleti Azzurri d'Italia was hours away from being called off due to heavy snow.
On-loan Inter Milan striker Marko Livaja opened the scoring but Marquinho pegged Atalanta back before Miralem Pjanic turned the game on its head with an exquisite free-kick, only for Livaja to net again for the home side heading into half-time.
Vasilis Torosidis waited for the snow to clear to head the winner and Atalanta promptly unravelled as Matteo Contini saw red following an unseemly scrap with Simone Perrotta.