On another night Leicestershire referee Kevin Friend might have penalised Newcastle's Kevin Nolan for his full-blooded tackle on Kyle Walker before Taylor pounced on the loose ball.
But it was another miserable result for opposite number Kevin Blackwell, whose injury-hit side were denied by Newcastle goalkeeper Steve Harper's world class save in the closing stages and have now lost their last four league matches.
The Blades slipped to 15th place, leapfrogged by arch-rivals Sheffield Wednesday on Saturday, and the former Leeds and Luton manager will now fear renewed pressure from the impatient Blades faithful.
Blades defenders Jordan Stewart and Andrew Davies returned to the starting line-up, while Fabricio Coloccini, Danny Simpson and Alan Smith were back for Newcastle.
Darius Henderson should have fired the Blades ahead in the third minute when springing the offside trap, but pulled his left-footed effort wide.
At the other end Newcastle striker Andy Carroll's shot was superbly blocked by Walker, but the home side set the early pace.
A sweeping Blades move ended with Henderson teeing up Keith Treacy, but the Irish winger's snapshot whistled over the crossbar.
Henderson then crossed for Stephen Quinn to shoot first time off target as Blackwell's side built up some momentum.
Newcastle midfielder Taylor later curled a right-footed free-kick high and wide and another last-ditch challenge from Walker denied Coloccini.
Blades striker Ched Evans was inches wide with his angled shot after bustling on to Bennett's long clearance as a highly-combative first period - Morgan and Newcastle pair Carroll and Taylor were all booked for fouls - ended goalless.
A more purposeful Newcastle twice went close to breaking the deadlock within eight minutes of the restart.
Nolan's curling shot was pushed away at full stretch by Bennett and Carroll's hanging header from Taylor's cross hit the woodwork.
But then Newcastle took the lead in fortuitous circumstances in the 54th minute.
Referee Friend adjudged Nolan's thumping challenge on Walker to be fair and with the defender prostrate, Taylor pounced on to the ball in space 25 yards from goal and unleashed a low right-footed shot that took a big deflection off Morgan to wrong-foot Bennett and nestle into the goalkeeper's bottom left-hand corner.
Walker limped off five minutes later and was replaced by Ryan France.
Treacy's quality cross was headed over by Stewart in the 61st minute as the Blades, roared on by most in a crowd of 26,536, battled gamely in search of an equaliser.
Evans' low free-kick was hoofed clear by Butt and visiting goalkeeper Harper blocked Henderson close-range effort.
Harper finished strongly - smothering Treacy's shot in injury time and then brilliantly denying Henderson's point-blank header as Newcastle held on.