Jedinak, who scored both of Australia's goals from the penalty spot in a 2-2 2018 FIFA World Cup qualifier draw against Thailand in midweek, played a full game as Villa picked up a creditable point.
Nathan Baker headed Villa in front on 20 minutes but striker Glenn Murray ensured a point for Chris Hughton's Brighton by replying just before the interval.
Villa top scorer Jonathan Kodjia twice saw headers pushed against the bar by Brighton goalkeeper David Stockdale as the visitors carried a greater threat in the closing stages.
Brighton, now unbeaten in nine matches, would have gone level on points with leaders Newcastle United with victory, but Villa were more than worth a share of the points before a season's best Amex crowd of 30,107.
Villa boss Bruce, winless in four previous visits to the Amex as a manager, made two changes with Ashley Westwood and Gabriel Agbonlahor coming into the side.
It was Agbonlahor's first start since March and the striker was almost put in the clear early on only for former Brighton loanee Gary Gardner to fail to control the ball on the edge of the area.
Villa keeper Pierluigi Gollini's handling was less than assured when winger Jiri Skalak curled a testing free-kick into the area.
But Villa went in front in the 20th minute when defender Baker headed his first goal for the club from 13 yards.
A foul by Anthony Knockaert on Gardner on the edge of the area gave Villa a free-kick and Baker rose to head in Albert Adomah's flighted delivery.
This was the first goal that Brighton had conceded in six-and-a-half hours and Albion had a let-off when sloppy play let in Agbonlahor, whose shot was blocked by Shane Duffy.
Home scoring specialist Murray drove Albion level on the stroke of half-time with his 10th goal of the season, all 10 coming at the Amex.
Murray, on a season-long loan from Bournemouth, fired low into the bottom right-hand corner after excellent link-up play with striker partner Sam Baldock.
Villa keeper Gollini flapped at a Skalak corner shortly after the interval moments after a teasing cross by Gaetan Bong eluded the Brighton forward line.
The Seagulls, beaten only once at home since New Year's Day, threatened when Murray rose early from a flick from Baldock but directed his header over.
Substitute Jordan Ayew put a deflected shot over for Villa before the recalled Westwood, in space on the edge of the area, drove over.
Albion keeper Stockdale kept his side on terms by turning a low shot from Adomah round the post on 70 minutes.
The Seagulls then had a let-off when, from Adomah's corner, Kodjia headed against the top of the bar.
Kodjia was unlucky again when a superb reflex save from Stockdale saw the striker's header come back off the bar nine minutes from time.