The Serbian striker converted Shane Ferguson's cross from close range to clinch Blues' first-ever points at the Riverside and their first victory on Boro soil in 14 attempts stretching back to a 1980 success at Ayresome Park.
More importantly the victory moves Lee Clark's side on to 49 points and into the top half of the table.
Either side could have claimed three points from a finely-poised encounter which lacked clear-cut chances, although Blues goalkeeper Jack Butland twice made impressive saves to deny Scott McDonald and Adam Reach.
Boro - playing in front of their lowest league attendance since October, just 14,348 - are now five points off the play-off places while they have lost four of their last five and won just one of their last seven.
Having started the year in third place they have now dropped down to ninth and had the season started on January 1 then they would be propping up the table.