Adam struck a free kick in either half to maintain the Light Blues’ unbeaten league run to eight games but Brown should have done better on both occasions.
He was badly out of position at the first goal as Adam swept his shot past him at the near post then allowed a strike from a similar position after the break to trundle agonisingly through his legs to extend Rangers’ advantage and give Adam his 10th goal of the season.
It was the perfect fillip for Walter Smith’s side ahead of the UEFA Cup tie with Osasuna later in the week and at a ground where Rangers have traditionally struggled in recent times.
Smith had made two changes to the team that had defeated Hapoel Tel-Aviv 4-0 at Ibrox 10 days previously.
Gavin Rae and Nacho Novo both dropped to the bench with the fit again Ugo Ehiogu and Adam reintroduced to the side.
It meant a return to midfield for Brahim Hemdani as Smith persisted with the 4-5-1 formation that has served the team admirably in recent matches.
Allan McGregor, despite his pending Euro suspension, kept his place in the side ahead of Stefan Klos.
Rangers had to avoid defeat to deny Celtic the chance to clinch the title in next week’s Old Firm game and made the perfect start when they went in front after just four minutes.
The goal stemmed from the genius of Adam. Lining up a free kick around 25 yards out after Kris Boyd had been fouled by Rob Jones, the former St Mirren man spotted Simon Brown drifting to the middle of his goal anticipating a cross.
Adam, instead, curled a fantastic shot into the near post, putting Rangers ahead and embarrassing the Hibs keeper in the process.
Having lost 2-1 on their previous visit to Leith – albeit several months and a regime change ago – Rangers seemed determined to make amends this time around.
Ex-Hibees Kevin Thomson and Ian Murray seemed unperturbed by the constant heckling to put in steady and efficient performances while Ferguson darted forward wherever possible to support lone striker Boyd.
Chances, though, for either side were rare. Ferguson hooked a shot goalwards that Brown saved comfortably before David Murphy dragged a free kick just wide of target after he had been fouled on the edge of the box by a combination of David Weir and Murray.
Adam almost repeated his trick with another sumptuous free kick but Brown was better positioned to grab his delivery this time as it arced once more towards the top corner of his goal.
Hibs began the second half with Benji on for Thomas Sowunmi and the Moroccan almost made an immediate impact when he connected well with Steven Whittaker’s cross but sent his volley narrowly over the crossbar.
The match turned on two incidents around the hour mark, the first a moment that Simon Brown will want to forget as quickly as possible.
Adam’s free kick seemed to lack the precision and pace to trouble the keeper but Brown, misjudging the flight, somehow allowed the ball to squirm out of his grasp and dribble through his legs to extend Rangers’ lead.
It was Adam’s goal but, just like his first, it came as a result of a howling error by the goalkeeper who thumped the turf in frustration at the costliness of his fallibility.
Hibs looked deflated and there was further anguish for the home side just minutes later when McGregor arched his body to expertly tip away Steven Fletcher’s goalbound drive.
It was a fine save that maintained Rangers’ dominant hold of this match and perfectly illustrated the contrasting fortunes of the two keepers.
Merouane Zemmama had a late shot cleared off the line by Chris Burke but by then the contest had been well and truly settled in Rangers’ favour.
RANGERS (4-5-1): McGregor; Hutton, Ehiogu, Weir, Murray; Burke, Ferguson, Thomson, Hemdani, Adam; Boyd (Prso 61)
Subs not used: Klos, McMillan, Novo, Rae, Lennon, Papac
Booked: Boyd (45), Thomson (61). Ferguson (85)
HIBERNIAN (4-4-2): Simon Brown; Whittaker, Hogg, Jones, Murphy; Sproule (Zemmama 69), Beuzelin, Scott Brown, Stevenson; Sowunmi (Benji 46), Fletcher
Subs not used: McNeill, Martis, Stewart, Lynch, McCann
Booked: Jones (41), Stevenson (58), Zemmama (86)
Ref: Charlie Richmond
Two goals and a decent all-round performance