But just when it seemed Town would have to settle for a point, Brkovic controlled Kevin Foley's 84th minute cross on his chest and found the net from just inside the penalty area with a superb overhead effort.
Teenager Calvin Andrew made his full league debut coming in for the suspended Howard and he almost made the perfect start when his ninth minute header from Paul Underwood's corner was hacked off the line by Ryan Brown.
Vale then threatened two minutes later when Jeff Smith ran past Brkovic and into the penalty area but saw his cross-shot saved at the near post by Marlon Beresford.
Both sides fought out a midfield battle until Andrew chased down an over-hit Sol Davis cross in the 23rd minute and pulled back for Kevin Nicholls to fire a 25-yard drive that was superbly tipped around the post by visiting goalkeeper Jonny Brain.
Andrew remained in the thick of the action as he shrugged off Steve Rowland to race clear down the left two minutes later, but his low cross just eluded the onrushing Brkovic in front of goal.
Hatters controlled possession without creating further clear-cut chances until Brkovic almost found an opening in the 58th minute, but after appearing to have a clear shot on goal 15 yards out, the Croat saw his effort blocked by Brown.
Luton continued to dominate and Stephen O'Leary saw his 10-yard volley bounce back off the bar after Vine's chip in the 76th minute.