Belgium boss Roberto Martinez opted not to pick any players with more than 50 caps during this international break, meaning Kevin De Bruyne, Romelu Lukaku, Eden Hazard, Dries Mertens, Yannick Carrasco and Thibaut Courtois were all left out.
Michy Batshuayi took advantage of the opportunity he was given with a great early goal, but Chiedozie Ogbene teed himself up for an overhead kick to equalise before half-time.
Hans Vanaken restored Belgium's advantage but substitute Browne powered in an 85th-minute header to secure a draw for Ireland in its centenary game.
Batshuayi fired Belgium into a 12th-minute lead when he cut inside of Seamus Coleman and curled a fine finish into the bottom-right corner from the left of the box.
The visitors struggled to create further chances despite controlling possession and their advantage vanished after Callum Robinson's cross was not dealt with and Ogbene converted an acrobatic finish.
Ireland would have moved in front two minutes after the restart were it not for a goalline block from Jason Denayer to stop Robinson flicking James McClean's strike home.
Shane Duffy did well to deflect a shot from Batshuayi wide but the resulting corner was nodded in by Vanaken with the help of a deflection off Coleman.
Belgium was unable to see out just a second win in five matches, though, as Browne's powerful header gave the Ireland fans late reason to cheer.