The Blades put in a polished display on Tuesday night to hand out a 2-0 defeat to Gary Megson's Baggies to regain top spot in Division One.
Warnock was delighted with his side's showing at The Hawthorns, and thinks it will be the catalyst to fire them towards promotion.
"It was a cracking performance, the team came of age," said Warnock.
"We are growing up all the time and we have produced some great away displays over the last 12 months.
"West Brom are a good side, it was a full house but we stood up to them and played some good football - it was a very satisfying win.
"Any team who finishes above West Brom will get automatic promotion."
West Brom boss Megson backed Warnock's men, saying that the South Yorkshire side were the best team his side had come up against this season.
"United are the best team we have played without a shadow of a doubt," said Megson.
"They are the best side I have seen in Division One."
Warnock now hopes his side can go one better than last season when a joyous campaign was soured with play-off heartbreak at the hands of Wolves in Cardiff.
Warnock, meanwhile, says that he hopes to welcome back Fulham's Jon Harley on loan once he recovers from a broken bone in his foot.
Harley will be missing for up to eight weeks but Warnock says he would like to bring him back to Bramall Lane on loan to help his recovery from injury.
"Fulham have had the injury looked at and discovered a small crack alongside one of his metatarsal bones and he has been ruled out from between six to eight weeks," said Warnock.
"We have told Fulham that when the problem has healed we will take him back to help him get fit and renew the loan deal."
