A pretty even first half ended goalless, as both teams had speculative efforts only at best.
Rothwell didn’t have to wait long in the second-half to break the deadlock, when a speedy counter attack led to a calm finish from Ade Ademidon on 46 minutes.
The goal seemed to spur the greens into life and they started to dominate possession and chances - Sam Wright stinging the gloves of the Rothwell keeper with another fierce shot.
It felt like an equaliser was inevitable and in the 74th minute, Ryan Rushen picked up the ball and curled a beautiful effort past the diving keeper from just outside the box.
Sleaford continued to push for the winner, with both Tom Ward and Mitch Griffiths seeing efforts clip the bar, while sandwiched between those efforts was a red card for the hosts following a poor challenge.
Then in added time came the decisive moment of the contest. A free-kick was awarded on the left hand side midway in the half, Griffiths stepped up and drilled a cross that clipped the head of the defender and nestled into the corner of the net. Ther was no question that it was on target, so Griffiths took the plaudits as Sleaford progressed.
Greens player-boss Ward, who had blooded several fringe players due to unavailability, said afterwards: “It was a good result, we dominated the 90 minutes and were well worth the win.
"We had seven lads missing today which created opportunities for others and it was great to see young lads playing so well.
"We know what to expect from the young lads, it’s about the more senior players stepping up and making sure the younger ones don’t go missing and I thought they were superb and it was a really well-won game.
"The next round isn’t until January so we can concentrate back on the league now and putting last Saturday right.”
The Greens return to United Counties League action by hosting Heanor Town at The Longwater Stadium on Saturday.