After Derek Riordan scored his fifth goal in four games on the stroke of half-time to cancel out Yoann Folly's first for the Dons, Scott Vernon bundled in a Paul Hartley cross which evaded a static Hibs defence after 62 minutes for the winner at Easter Road.
The result took Brown's side three points clear of Tuesday's opponents Hamilton at the bottom of the SPL and within two points of free-falling Hibs.
In Colin Calderwood's first match in charge on October 23, Hibs conceded four goals in the opening 61 minutes before falling 4-2 to the Dons at Pittodrie.
It was Aberdeen's most recent win, a run which contributed to the departure of Mark McGhee.
Former Scotland boss Brown's scheduled first match in charge - last weekend against his former club Motherwell - was postponed due to the Arctic conditions which have swept Scotland.
And with Hamilton's clash at Dundee United - the Dons' next two opponents - postponed by the elements today, Brown knew a point would take his side off the foot of the table ahead of the midweek meeting with Accies.
Hibs now host Dundee United having now claimed two wins and a draw in nine matches under Calderwood.
Chris Maguire fired over after three minutes before Jamie Langfield smothered an effort from Riordan after Liam Miller's lofted ball into the area.
Derek Young tested Mark Brown from the edge of the area before the Hibs goalkeeper was beaten after 36 minutes.
Vernon out-muscled the returning Chris Hogg on the left side of the area to take possession and crossed to the far post, where the late-arrival of Folly surprised Hibs' defence and the midfielder tucked in.
But the hosts levelled in the opening minute of stoppage time at the end of the first half after Langfield parried John Rankin's cross-cum-shot from the left of the area and the ball dropped for Riordan to net from three yards out. It was his eighth goal of the season.
Mark Brown twice denied the Dons early in the second period, saving Paul Hartley's free-kick and substitute Josh Magennis' point-blank header.
Magennis then, despite no contact, went down looking for a penalty under Mark Brown's challenge after dispossessing Hogg, the club captain but making only his third appearance under Calderwood and enduring a torrid time. Magennis avoided a caution for simulation.
Valdas Trakys and David Wotherspoon went close before the Dons scored a second after 62 minutes.
A right-wing cross from former Hibs and Hearts midfielder Hartley evaded the hosts' defence and Vernon bundled the ball in from five yards out.
Wotherspoon mis-hit a shot as Hibs had an immediate opportunity to respond before Mark Brown saved from Magennis.
Miller was replaced by Danny Galbraith with 19 minutes remaining and the substitute immediately crossed for Riordan to fire narrowly wide.
Colin Nish replaced Trakys as Calderwood sought fresh legs in attack, but the supply remained poor.
Mark Brown saved a long-range Maguire shot before Ian Murray was played through by Riordan, but Langfield saved well.
Aberdeen scrambled clear the resulting corner as they savoured a fourth win of the season.