Following 23 years as assistant boss to Jim Jefferies, including two spells at Hearts and one at Kilmarnock, caretaker boss Brown was seeking to prove his credentials as long-term successor to Colin Calderwood.
It was not an entirely convincing performance as Manuel Pascali put the visitors in front after 36 minutes before half-time substitute Leigh Griffiths equalised after 50 minutes to earn Hibs a point.
Hibs are seeking a successor to Calderwood, who was sacked on November 6, a day after the 1-0 loss to Dunfermline.
Brown has already been interviewed by the Hibs board, who are seeking their fifth manager in four years and are also reportedly considering Bohemians' Pat Fenlon and Michael O'Neill of Shamrock Rovers for the position.
Prior to the match Brown insisted he did not wish to be judged on one performance and whether there were enough positive signs to convince the board he is the right man remains to be seen.
Killie were the visitors to Easter Road the last time Hibs were without a permanent boss, when last October the hosts triumphed between the departure of John Hughes and the start of Calderwood's ill-fated reign, which yielded 12 wins in 49 matches.
Brown, who began the season as assistant manager at Hibs' Edinburgh rivals Hearts, has recognised his charges are seen as a soft touch and lack a competitive instinct, urging his players to take more responsibility.
Conceding the first goal was a hallmark of Calderwood's 12 months in charge and the Pars netted after three minutes in the final fixture of his spell as boss.
Brown took a defensive approach, with a midfield five and Garry O'Connor on his own up front.
Both sides struggled to get a meaningful hold on proceedings and midfielder Dean Shiels attempted to spark the game into life midway through the first half, weaving his way into the left of the area and cutting onto his right foot, but Graham Stack held the shot at his near post.
Killie took the lead after Hibs failed to clear a corner. Stack could only push away a stinging drive from Danny Buijs and Pascali tapped in the follow-up.
Boos - a common occurrence over the last 18 months of misery at Easter Road - rang out from a minority of supports at the interval.
Brown reacted by making two changes at half-time, introducing Griffiths for Danny Galbraith and Richie Towell for Michael Hart, while Killie replaced striker Paul Heffernan with Gary Harkins.
Griffiths, who had been ill during the week, joined O'Connor up front and the on-loan Wolves striker's impact was swift as he equalised five minutes after being introduced following a strong run by Ivan Sproule.
Jaakkola palmed away Sproule's attempted cross and Griffiths collected on the left before netting off the post from an acute angle.
Griffiths prodded wide after surging into the right side of the box before O'Connor shot tamely from 30 yards.
Stack saved a Shiels effort at his near post and Liam Kelly shot wide from long range.
Wotherspoon was cautioned for a late tackle on substitute Matthew Kennedy but Harkins' header from the resulting free-kick lacked the pace to trouble Stack before Isaiah Osbourne was also shown a yellow card for a poor tackle.
Shiels chipped onto the top of the Hibs net with an audacious effort and James Dayton's snap shot on the turn was hit straight at Stack as the match ended level.