Newcastle climbed back to the summit courtesy of a lucky own goal after Ryan Taylor's low 25-yard shot deflected off hapless Blades captain Chris Morgan and into the bottom corner to heap more pressure on the hosts' manager Kevin Blackwell.
Asked whether his side were fortunate to leave with a win, Hughton said: "No. What we have had is Steve Harper who has made a couple of absolutely fabulous saves and that's the quality of the keeper he is."
Hughton added: "He's doing the business. There's different aspects to Steve Harper. He's a Newcastle lad and has been here for a long time, he's a very calming influence, a mature lad and a mature player and that has been invaluable for us.
"But over the 90 minutes we deserved what we got. It was vitally important we got something from the game."
Hughton dismissed suggestions Leicestershire referee Kevin Friend might have blown for a foul in the build-up to the game's only goal when Kevin Nolan clattered into Blades defender Kyle Walker, leaving the ball to break free into Taylor's path.
Hughton, marking his first game as permanent manager with his side's third win in seven league matches, said: "My first impressions are that he won the ball."
Both sides created several other goalscoring chances. Blades goalkeeper Ian Bennett saved well from Nolan's curling shot early in the second half and Newcastle striker Andy Carroll's header soon after hit the woodwork.
At the other end Henderson should have given the Blades an early lead, but pulled his angled shot wide, while Harper denied Keith Treacy in fine style as well as keeping out Henderson's last-gasp header.
Lady Luck still refuses to smile on Blackwell, who was somehow still able to smile, suggesting he must have run over a black cat after what he described as a series of harsh decisions, another injury - this time to the impressive Walker - and a fifth yellow card for Chris Morgan.
The Blades captain will now miss next Monday's derby clash with former club Barnsley, while just as worrying for Blackwell is the sight of Sheffield Wednesday lying above his side in the table.
Blackwell, who moaned he was now without 14 players from a 25-man first-team squad, said: "I'll admit it, I ran over a black cat about a month ago. I thought I got away with it, but I've been found out.
"What can you do? That's just typical of the last few weeks. Goals have gone in off someone's backside and it was a foul on Kyle Walker.
"But you don't get those decisions. I don't know. Then it's come in and Morgs has deflected it in.
"There wasn't much wrong today. I thought we played very well. It was a top performance from a side that's a little bit short on luck at the moment."