Clarke opened the scoring in the 14th minute with a close-range finish and struck an 87th minute winner after Franck Moussa's shot was parried by George Long. Sandwiched in between Clarke's double-strike was Dave Kitson's headed equaliser from Barry Robson's corner after 72 minutes.
Robins said: "All in all it was a great win. I'm delighted with them because they worked really hard.
"In the first half I thought we were brilliant. In the second half we were not as good but we came out on top.
"Sheffield United are a really good side and they put you under unbelievable pressure with the balls they pump in and we dealt with it for most of the night.
"Then we got a little bit ragged and they put us under pressure so we just tried to tighten it up a bit."
Sheffield United boss Danny Wilson was disappointed to see his side slump to a third straight home defeat following a strong second-half performance.
Wilson said: "It always feels a bit difficult to take when you've played well in the second half and been punished by one misdemeanour I suppose.
"In the first half we weren't at the races at all, I'll be quite honest, but in the second half it was quite the opposite.
"It was one-way traffic in the second half and we got back in the game. We felt the ascendancy was ours and we felt we could go on and win the game."
- Sports & Recreation
- Sheffield United