Reigning champion Lucas di Grassi of Brazil, who had scored only three points prior to Saturday, was second for the Audi-backed Team Abt after failing to find a way past Vergne in a race-long battle.
Britain's Sam Bird completed the podium for DS Virgin Racing.
Di Grassi had originally secured pole position but was demoted to second when the top four in qualifying were handed penalties just before the race following a stewards' investigation for cutting a chicane.
"We had the fastest car but really it was going to be a crash or we stay as we are," said the Brazilian of his efforts to pass Vergne.
Jaguar Racing's New Zealand driver Mitch Evans finished fourth after being sent to the back of the grid for weight distribution discrepancies.
The next round is in Rome on April 14.
(Reporting by Alan Baldwin, editing by Ed Osmond)
