Sone Aluko gave Aberdeen an early lead but Motherwell fought back quickly and the impressive Jeffers headed a 14th-minute equaliser.
And the visitors triumphed in a bad-tempered second half, which saw home skipper Paul Hartley sent off for lashing out at Keith Lasley, when Jamie Murphy punished some slack defending.
The victory moved Motherwell up three places to fifth, eight points ahead of their opponents, and the performance of Jeffers will give them added hope of sealing a top-six place.
The former England striker looked sharp and intelligent on and off the ball after being quickly promoted following his 15-minute debut in Saturday's 6-0 defeat by Rangers, with the injured Steve Jones dropping out.
The game had originally been scheduled as Brown's first in charge but was delayed by snow, allowing Nick Blackman to line up against his former Motherwell team-mates after the Blackburn striker followed the veteran manager to Pittodrie.
The postponement also spared Brown a likely backlash with only about 100 Motherwell fans making the midweek trip up in wet conditions.
They were probably wishing they had stayed at home after two minutes when Aluko collected Steven Smith's cross and flicked the ball over Stephen Craigan's head before dispatching the ball in off the far post.
But Motherwell twice forced Jamie Langfield into saves before the 10-minute mark with the Aberdeen goalkeeper tipping over Ross Forbes' curling free-kick and beating away Murphy's powerful long-range strike.
And Langfield was helpless when Jeffers glanced a header into the top corner from 14 yards following Craigan's driven cross.
The former Arsenal forward soon saw a shot blocked following Murphy's cross and Aberdeen quickly came close when Scott Vernon glanced David McNamee's cross just wide.
Jeffers again threatened when Langfield tipped his curling 20-yard strike wide.
Motherwell were moving the ball around impressively and both John Sutton and Jeffers got on the end of Tom Hateley crosses but were put under just enough pressure to negate their efforts.
Hartley drove just wide from 25 yards but Motherwell continued to edge possession and Murphy fired inches over from similar range.
Jeffers forced another save from Langfield after beating two men, but Motherwell had a let-off when Darren Randolph fumbled Vernon's long-range strike inches wide.
The visitors were last to threaten before the break when Jeffers and Murphy broke well to set up Shaun Hutchinson, who stabbed the ball straight at Langfield.
Aluko had a clear sight of goal but fired against a defender and a previously mild-tempered game boiled over 10 minutes into the second half.
Lasley sparked a mass rumpus when he led with his elbow in an aerial challenge with Hartley, who responded by booting the Motherwell midfielder in the chest.
Steven McLean showed a red card to Hartley and yellows to Lasley, Langfield and Craigan, and Forbes was soon booked for an innocuous challenge. Lasley had already been nursing bruised ribs and made way for Stevie Hammell, while Humphrey replaced Jeffers.
Motherwell's man advantage was not immediately apparent but they regained control midway through the half and Langfield parried well after Sutton met Humphrey's cross.
The winner came in the 71st minute when Murphy burst on to Zander Diamond's misplaced header and held off Nikola Vujadinovic before finding the far corner from just inside the box.
Vernon fired wide following a corner and tempers were soon frayed again when Hateley tripped Maguire off the ball after being incensed by the forward's theatrics.
Both players were booked and the Motherwell full-back soon avoided further punishment when he brought down the Scotland international.
Aberdeen pushed for an equaliser but Murphy came closer to scoring after a brilliant last-minute run before his shot was cleared off the line.