The Democratic Party (PD) won support from 28.1 percent of people polled on their voting intentions - a rise of three points over a week - while Berlusconi's People of Freedom (PDL) party dropped 1.7 points to 26 percent, according to the SWG poll.
The poll followed a huge upswing for the left at local elections last weekend, in which they took most battleground areas, including the capital Rome.
The SWG figures show the centre-left is finally winning back some of the support lost after a pitiful performance at general elections in February lead to a damaging political stalemate.
But the lead is still narrow.
The PD and its main ally, SEL, would win 32.9 percent of votes at early elections according to the poll, while the PDL and allies including the Northern League would snap up 32.4 percent.
The Five Star Movement (M5S), which soared in popularity earlier this year on the back of protest votes, slipped two points to 17.9 percent following a disastrous performance at the local elections.
The movement is currently struggling with an internal division between those who unquestioningly support its founder, brash comic Beppe Grillo, and those who criticize his monopoly of the group and refusal to consider working with the other political parties.
According to political observers, Five Star members are increasingly turning against Grillo, who lashes out publicly at anyone seen to be criticizing him or his methods.
The SWG poll said the most popular political personality was Matteo Renzi, 38, the young and dynamic mayor of Florence, who is seen by many as the future head of the PD and whose popularity rating stands at 60 percent.
At the other end of the scale, Berlusconi's popularity rating was 26 percent, it said.