Sharp made it 19 goals for the season while City striker Teemu Pukki took his tally to 18 as two of the division's leading sides produced a match worthy of the occasion.
Norwich were quickest out of the blocks, piling on the pressure and forcing a series of early corners before deservedly taking the lead in the 11th minute.
Winger Onel Hernandez had already tested Dean Henderson from distance and made no mistake after a neat one-two with Pukki, calmly slotting the ball through the keeper's legs to open the scoring.
The Canaries continued to press, with Mario Vrancic sending a header just wide from an Emi Buendia corner, but the Blades gradually got a foothold in a game that was keenly contested from the word go, with strong tackles flying in from both sides.
Their first sight of goal came after 22 minutes but a slick move down the right ended with Kieran Dowell slicing the ball wide from a decent position while it needed a fine block by Tom Trybull to keep out Gary Madine's on-target effort a couple of minutes later.
However, it was Norwich who nearly doubled their advantage five minutes before the break.
Buendia worked himself a clear sight of goal after linking up with Marco Stiepermann but his effort from just outside the six-yard box sailed over, via a slight deflection off the keeper.
The hosts had marginally the better of a breathless first half but were pegged back deep into injury time after sloppy defending saw them concede a penalty.
Buendia did well to track Enda Stevens' run into the area but pulled him down as he prepared to cross and referee James Linington had no hesitation in pointing to the spot.
After a delay, which saw keeper Tim Krul yellow carded for time-wasting, Sharp made no mistake from the spot.
The visitors had a chance to get their noses in front in the opening minute of the second half but Sharp's close-range header was inches too high, clipping the crossbar as it went over.
John Fleck then curled a 25-yard effort just wide as Chris Wilder's side continued to press.
But it was Norwich who scored the crucial third goal of the game after 56 minutes through top-scorer Pukki.
When the ball found its way to Max Aarons on the right, the defender delivered a cross that the Finnish striker coolly chipped into the back of the net with a delightful first touch.
The Blades replied immediately, with Madine firing in a rising shot from distance that Krul did well to tip round the post, but Norwich were generally looking reasonably comfortable as the game entered its final quarter.
Wilder's men kept plugging away however and got their reward 12 minutes from time as Sharp doubled his tally with a firm back-post header after being picked out by an excellent cross from the right by substitute Mark Duffy.
It was now anyone's game, with play swinging end to end amidst a cracking atmosphere generated by a crowd of nearly 27,000, but 2-2 was the way it ended, with no further clear-cut chances.