The Tykes hit back at Oakwell to extend their unbeaten run to eight in the Championship.
Argentinian midfielder Colace raced into the penalty area in the 59th minute to meet Daniel Bogdanovic’s cross and head in a fine winner for Barnsley, who fully merited their fourth home league win of the season.
Middlesbrough, who were without the suspended Leroy Lita and unwell fellow striker Dave Kitson, had taken a fortuitous lead midway through the first half through Justin Hoyte, whose attempted cross flew into the top corner.
But Tykes captain Stephen Foster headed in at the far post early in the second half before Colace’s well-crafted winner.
The visitors have now won only twice in 10 under Strachan.