Juventus, Roma and Napoli hit 11 goals between them to deliver a blow to pursuers Fiorentina and Verona as Milan were stunned 4-3 thanks to four goals from teenage striker Domenico Berardi on Sunday.
Juventus had been looking for a club record of 11 successive wins and despite conceding a 21st minute opener to Mauricio Pinilla the champions fought back in clinical fashion with Fernando Llorente netting twice in a 4-1 win at Cagliari.
Conte said he was "proud" to become the first Juve coach to reach the milestone, but added to Sky Sport Italia: "I thanked all of the team for helping us reach this milestone but we have to try and extend this streak or another side will try to overtake us."
Roma began the day eight points behind leaders Juve but had little trouble dispatching Genoa, who were reduced to 10 men before the hour, 4-0.
Alessandro Florenzi led the rout with a sublime overhead kick, with further goals coming courtesy of club captain Francesco Totti, Maicon and Mehdi Benatia.
Totti, hitting his first goal in nine months, hailed Juve's campaign but said the title race was not over.
"Juventus are the reigning champions and they're almost a class apart, but we have a strong side that won't quit. Until the very end, we will be giving them a hard time," Totti told Sky Sport Italia.
Napoli were two points further adrift but despite a potentially tricky fixture returned from high-flying Verona with a precious 3-0 win.
Napoli coach Rafael Benitez suggested the scoreline flattered his side, which is still missing Marek Hamsik, Juan Zuniga and goalkeeper Pepe Reina among others, due to injury.
"It was a difficult game but we showed that we are a strong team," said the Spaniard, admitting their next major aim comes at home to Roma, on March 9.
"The home game against Roma is our next major objective but we have our own path set out and we'll see where it takes us."
In Sunday's late game Japan international Keisuke Honda came off the bench to make his debut for Milan only to see the struggling Serie A giants stunned 4-3 away to Sassuolo, with all four of the hosts' goals coming from teenage striker Domenico Berardi.
Robinho gave Milan a ninth-minute lead, beating Gianluca Pegolo with a low angled strike at the keeper's far post and Mario Balotelli made it 2-0 four minutes later.
Sassuolo, however, had other ideas, showing great resolve to reduce their two-goal deficit within 13 minutes thanks to Berardi, who completed his hat-trick on 41 minutes and hit his fourth minutes after the restart.
"It's a match I won't ever forget," said 19-year-old Berardi, who is on loan from Juventus but quickly dedicated his feat to Sassuolo coach Eusebio Di Francesco.
"He took us from Serie B to Serie A, and has a big heart just like the rest of us."
Milan coach Massimiliano Allegri sent on Honda 20 minutes into the second half and the Japanese saw a header from a cross on the left blocked by Pegolo and then struck the post with a first-time curling effort from the edge of the area.
Milan were given a glimmer of hope five minutes from the finish when Montolivo collected De Jong's ball in midfield and struck a long-distance drive which beat Pegolo low at his far post.
But Milan spurned another late chance when Balotelli's header at the back post was punched out by Pegolo and Giampaolo Pazzini followed up by sending the rebound against the crossbar.
"It's a terrible defeat for us, we just weren't good in defence," said Allegri. "Perhaps we were a bit unlucky at the end but it's a match to forget."
Milan remain 11th, now 30 points behind Juve and 20 behind Napoli in the first Champions League qualifying spot.