Summer signing Oscar scored twice in quick succession to put the Blues in charge, the 21-year-old Brazilian opening the scoring with a deflected strike in the 31st minute before doubling Chelsea's lead almost immediately with a stunning 25-yard effort.
However, Juventus, back in the Champions League for the first time since 2009, pulled a goal back through Arturo Vidal before the break and Fabio Quagliarella levelled the scores up 10 minutes from time to earn the Italians a point.
Also in Group E, Henrikh Mkhitaryan scored twice to give Shakhtar Donetsk a 2-0 win over FC Nordsjaelland.
Barcelona avoided a shock at home to Spartak Moscow as Lionel Messi scored twice in the final 19 minutes to earn them a 3-2 victory.
Cristian Tello put Barca ahead in the 14th minute but an own goal from Dani Alves and a second-half strike from Borges Romulo saw Spartak turn the game on its head and leave the Nou Camp shellshocked.
Messi, as he so often is, was Barca's hero though as he scored in the 71st and 80th minutes to leave Tito Vilanova's men top of Group G, with the other match seeing Celtic and Benfica draw 0-0.
In Group H, Manchester United edged past Galatasaray 1-0 at Old Trafford thanks to Michael Carrick's seventh-minute goal. United had the chance to make it more comfortable for themselves but Nani saw a 52nd-minute penalty saved.
United are now second behind behind CFR Cluj, who beat Braga 2-0 away following a classy first-half brace from Brazilian striker Rafael Bastos.
In Group F, Bayern Munich and BATE Borisov both started their campaigns with victories.
Bayern beat Valencia 2-1 with Bastian Schweinsteiger and Toni Kroos on the scoresheet for the Germans with the Spanish side pulling a goal back late on through Nelson Haedo Valdez.
Bayern also missed a last-minute penalty through Mario Mandzukic after Valencia defender Adil Rami had been sent off.
Belarusian champions BATE saw off Lille with a blistering first-half display tro win 3-1.
Alexander Volodko swept the visitors in front with just six minutes on the clock with a superb lofted finish over Mickael Landreau, and further goals from Vitaly Rodionov and Edgar Olekhnovich effectively ended the contest before half-time.
Aurelien Chedjou reduced the deficit just before the hour mark but the French side could not get any closer.
Wednesday's Champions League Results