Motherwell frustrated Hibs for long spells, but after Brown's 65th-minute opener, it looked as if there would be only one winner.
Rob Jones threatened early on from a looping cross from Steven Whittaker, but he could get no power on his header.
There was a scare for the home side when goalkeeper Andy McNeil misjudged the flight of the ball, but the angle was too tight for Richie Foran and he could only send his header behind.
Hibs' best first-half move came when a back-heel from Steven Fletcher released Lewis Stevenson, but his cutback was dealt with by Foran before the home side could take advantage.
Ivan Sproule had another darting run at the Motherwell defence but Stephen Craigan was alert to the danger and made a timely intervention.
Fletcher then tried his luck with a first-time shot from the edge of the area which Graeme Smith needed two attempts to gather.
The Hibs striker got his head to a Sproule cross late in the first half, but there was no power and again Smith collected comfortably.
Brown scored the opener after 65 minutes when he slotted the ball home from 16 yards after great work by Sproule.
Sproule also set up the killer second in injury time, as Benjelloun shot in from an acute angle.