The visiting Blues grabbed a vital away goal as former boss Jose Mourinho and his Inter side came out on top in a pulsating clash at the San Siro.
Chelsea, whose defeat was compounded by the loss of goalkeeper Petr Cech with a calf injury in the second half, were a goal down inside three minutes when striker Milito put Mourinho's side ahead.
Salomon Kalou equalised in the 51st minute but Inter restored their advantage four minutes later when Cambiasso drilled in the winner.
Kalou's goal may yet prove to be the pivotal moment of the tie when the two teams meet again in the return leg at Stamford Bridge next month.
A match that had been built-up as a contest between the two coaches - Blues boss Carlo Ancelotti, of course, was returning to his former home - was sparked into life inside three minutes.
Thiago Motta's throughball found Milito inside the Chelsea penalty area and when captain John Terry half-heartedly attempted to block Milito's progress, the Inter striker slammed the ball beyond Cech at the near post.
Mourinho greeted the goal with an approving nod from his seat in the Inter dugout.
In the 11th minute, Nicolas Anelka tried his luck with an angled drive but the France international could only find the side netting.
But overall Chelsea's response to their early setback had been promising and moments later Kalou brought a save from Julio Cesar with a speculative 25-yard drive.
Chelsea won a free-kick some 35 yards out when Dejan Stankovic fouled Ballack in the 15th minute and they were unlucky not to equalise.
Drogba's fierce attempt on goal cannoned back off the crossbar with Cesar well beaten.
Ballack then forced Cesar to punch clear with a swerving 18-yard drive.
In the 22nd minute goalscorer Milito was booked for diving after going down from an imaginary challenge by Ricardo Carvalho and Kalou followed him seconds later after a foul on Wesley Sneijder.
The early goal had sparked Chelsea into life and the game was hardly the defensive lockout many had predicted.
Apart from Milito's goal, Chelsea had looked untroubled in defence and had dominated possession.
John Obi Mikel sent a rising drive into the arms of Cesar in the 29th minute as Chelsea continued to press for a leveller.
But Inter spurned a gilt-edged chance to increase the lead in the 34th minute when Sneijder's cross found Eto'o unmarked on the edge of the six-yard box.
But instead of planting the ball past Cech, Eto'o completely missed his kick.
Chelsea should have been awarded a penalty seconds before the interval when Kalou went down under a challenge from Walter Samuel.
But their penalty claims were denied and referee Manuel Gonzalez was surrounded by Chelsea players at the half-time whistle.
But in the 51st minute Chelsea were level through Kalou. Branislav Ivanovic created the opportunity when he ran unchallenged to the edge of the Inter penalty area.
The Chelsea right-back looked to have over-run the ball but somehow managed to turn it into the path of Kalou, who curled it in from the edge of the box.
Kalou and the rest of the Chelsea squad then ran to the dugout in a clear show of support for coach Ancelotti.
It took Inter just four minutes to re-establish their lead.
Ivanovic blocked Cambiasso's first attempt but there was little anyone could do about the follow-up shot which flashed into the bottom corner beyond Cech from 18 yards.
It got worse for Chelsea on the hour when goalkeeper Cech damaged his knee after rolling the ball out and had to be stretchered off.
There was nobody around the Czech Republic international when the incident occurred.
He was replaced by Hilario but it was another blow to the Blues who were struggling to get back into the game for a second time.
Chelsea should have levelled in the 64th minute when Lampard collected a cross from Anelka but saw his eight-yard shot saved by Cesar.
The Premier League title hopefuls were virtually camped inside the Inter half in the last 10 minutes but with Kalou now replaced by Daniel Sturridge, they had little outlet on the left.
Mikel summed up a night of frustration for the Blues when he sent a 20-yard shot into the stands in the 88th minute.
Inter, having been outplayed all night, hung on to record a first-leg victory but the Mourinho bandwagon will role into Stamford Bridge next month with double the intensity.