The 35-year-old midfielder, who will join Aberdeen as player/assistant next season, turned in a steady but unspectacular performance in an encounter the Parkhead club dominated without getting a goal for their efforts.
As Brown bid farewell to the Hoops after 14 years at Parkhead, a dismal season ended for the Glasgow side, who continued to search for a new manager, with Eddie Howe still the frontrunner.
Hibs confirmed their third-placed finish in the Scottish Premiership with a win at Aberdeen in midweek and their much-changed line-up in the final game of the season reflected their participation in next week's Scottish Cup final against St Johnstone at Hampden Park.
But they were fitting opponents for Brown's Celtic swansong. His last game for Hibs before joining Celtic for £4.4million in 2007 had been an end-of-season win over the Hoops at Easter Road.
However, it was very much a second string Hibs side.
Jack Ross left out eight players, including attackers Martin Boyle, Christian Doidge and Kevin Nisbet, who will possibly start next week's showpiece, with Israel goalkeeper Ofir Marciano playing his last game before he departs the Leith club after five years.
The visitors, understandably, looked more cohesive.
Elyounoussi, twice, and Parkhead midfielders David Turnbull and Callum McGregor all had efforts saved by Marciano as Celtic dominated possession.
Then Hoops attacker Ryan Christie had a long-range effort fly past a post.
The French forward was not as successful with his second attempt, hitting the wall.
Marciano almost casually punched away a 20-yard drive from Elyounoussi in the 54th minute as Celtic's domination continued after the break.
Leigh Griffiths and Forrest replaced Edouard and Christie on the hour mark, with Hibs hemmed in by sheer pressure of Celtic's pressing.
Ross responded by beefing up his side.
And the home defence remained firm, with Marciano foiling Forrest from close range.
Celtic will look to re-set under a new boss in the summer, while Hibs can now look forward to their trip to Hampden.