Both sides had chances early on with Luke Moore dragging a shot wide and Matty Oakley firing over from 20 yards before Wayne Brown blocked Moore's goal bound drive.
Moore continued to menace City and should have done better on 18 minutes when he fired Gianni Zuiverloon cross straight at the keeper.
Scott Carson was then quickly off his line to foil Martyn Waghorn who had been put through by Matt Fryatt.
Carson was in action again soon after when he got down well to keep out Waghorn's shot on the turn from 12 yards.
Albion took a 37th minute lead when Dorrans drove a low 25-yard free-kick through a crowded penalty area into the left hand corner of Chris Weale's goal.
And the Baggies doubled their lead on 40 minutes when Jara scored from 30 yards with a shot which curled away from a diving keeper.
Leicester should have pulled a goal back within seconds of the restart when unmarked substitute Paul Gallagher failed to connect with Fryatt's cross to the near post.
City then squandered another good chance when Waghorn set up Berner who sidefooted wide from 12 yards.
But Albion continued to look the more dangerous with Weale having to be at his best to keep out a Chris Brunt header.
City increased their work rate to stem Albion's flowing football and impose themselves on the game, but they struggled to make much of an impression against the visitors' solid defence.
And Albion almost notched a third late on when Moore latched on to a Scott Carson clearance then lobbed the City keeper with the ball bouncing off the bar to safety.
City scored a consolation goal in time added on when Carson failed to keep out Gallagher's long-range free-kick and Berner was on hand to bundle home the loose.