Lee Erwin and Stephen McManus had the visitors two up before half-time and Lionel Ainsworth looked to have ended any hopes of a Rangers fightback when he struck the third shortly after the interval.
But Darren McGregor’s header late on brought the Steelmen back down to earth. Baraclough lavished praise on his charges but warned there’s still plenty of work to be done.
“To a man the lads were fantastic,” he said. “We have come here with a game plan, drawing them on and then countering with pace. We did that fantastically well.
“We could have had a couple more but I can’t fault them when they’ve scored three goals away from home.
“They dealt with the crowd and with the magnitude of the situation. We were fantastically calm when Rangers put the pressure on with balls into our box.
“We will have to wait and see if 3-1 is enough. To have a two-goal lead is great but we now have to work even harder than we did tonight to make sure get over the line.
“It’s not going to be easy. No-one in our dressing room is kidding themselves, none of them are celebrating tonight. All the cliches are true – it’s just half-time.”