The Argentine midfielder netted the game's only goal shortly before the break, firing home a superb driven cross from Jim O'Brien to secure Barnsley's first win over United in nine attempts.
The Tykes are in the midst of their best run for a year and the victory extended their unbeaten record to five Championship matches, as well as increasing their gap over United to seven points.
Barnsley looked indomitable throughout and rarely looked under threat from United, whose manager Gary Speed is subject of rife speculation linking him with the vacant Wales job.
Heading into the clash, adversary Mark Robins made just one change to the Barnsley side that drew with Watford a fortnight ago, with Nathan Doyle seizing Diego Arismendi's holding midfield role.
The Blades, meanwhile, handed a debut to experienced former England international goalkeeper Richard Wright.
Wright was one of several changes made by manager Speed, with Johnny Ertl, Jean Calve, Andy Taylor and Mark Yeates all returning to the starting line-up.
Both sides attacked with intent from the offset but the first real chance of the match came from a set piece, with Adam Hammill whipping a 25-yard free kick just over the bar.
The former Liverpool trainee's 10th minute effort spurred the Tykes into life, with a goal-bound drive from Doyle smartly blocked by Kyle Bartley five minutes later.
Barnsley continued to run proceedings but the visitors almost capitalised on their inability to break the deadlock, with Taylor's audacious long-range effort coming close.
The home side had their own daring effort from distance on the half hour mark, with O'Brien turning smartly before lashing over from the edge of the box.
O'Brien made amends in the 37th minute by setting up the opening goal, driving across a superb right-wing cross that Colace smashed home from close range.
With the first half having petered out, the Blades' hopes of responding after the restart received an early blow when Wright saw his Blades debut curtailed by injury.
Regular custodian Steve Simonsen came on to replace the 33-year-old and was quickly forced into action, preventing Hammill from extending the home side's lead.
Minutes later Simonsen did well again to palm wide a rasping drive from left-back Bobby Hassell as the Tykes looked to double their advantage.
The home side continued to look dangerous on the attack as the Blades pressed forward in search of a much-needed equaliser.
Despite the raucous support of the 2,003 visiting fans, an equaliser proved elusive as Barnsley's resolute defence held off United's late barrage.