Goals to Frank Lampard and Michael Ballack either side of half-time secured a 2-0 win for Chelsea, but things may have been different had the Blues stand in keeper not saved Danny Webber's weak spot kick in the 17th minute.
Chelsea striker Didier Drogba had brought down Claude Davis in the box with referee Martin Atkinson pointing to the spot to allow the newly promoted Sheffield United a rare opportunity of having a free shot on the League champion's goal.
However Hilario, who was deputising due to Petr Cech's skull fracture and Carlo Cudicini's concussion, guessed correctly and dived to his left, easily saving Webber’s soft, side-footed effort to keep the score 0-0.
The scare woke Chelsea who knuckled down, and after a Sheffield United foul, Frank Lampard scored with a cracking free kick from 25 meters, sending United keeper Paddy Kenny the wrong way.
It was a cruel blow for the home side who had been well in the match with just two minutes left to play in the first half.
Then, three minutes into the second half Lampard provided a cross from the left for midfielder Ballack to head home at the far post to make it 2-0.
Jose Mourinho, Chelsea manager, was pleased his team got the points on the day, but was still upset about the penalty awarded against his team.
"The decision for me was completely wrong," Mourinho told Sky Sports.
"It was a big decision against Chelsea at the beginning of the game. If Hilario doesn't save it maybe we are in trouble.
Frank Lampard (L) celebrates his
screamer with Arjen Robben
"It was not easy for us but the team fought well. We deserved the victory and could have scored more goals."
Sheffield United tried hard but were outclassed in what is their sixth loss in 10 league games, capping another dismal day for the club who on Friday denied reports that Davis had pulled a razor blade on team-mate Ade Akinbiyi during a training ground bust-up.
"Goals change games and it really would have been nice for once to put a penalty away and put a bit of pressure on them, take the lead and see how they reacted," Sheffield United boss Neil Warnock said.
"Unfortunately it was not to be and a goalkeeping error resulted in the first goal.
"I'm disappointed with the result but it augurs well. I think we've got a fighting chance (of staying up)."
Rooney runs riot
Meanwhile, Wayne Rooney broke his goal scoring drought with a hat-trick of clinical finishes as Manchester United remained top of the table on goal difference after a 4-0 away win over Bolton at the Reebok Stadium.
Rooney opened the scoring in the 10th minute and followed up with his second six minutes later after latching on to a Michael Carrick pass from deep.
Up, up, and away: Wayne Rooney
the hat-trick hero for Man United
Red Devils midfielder Cristiano Ronaldo marked his return from a virus with a goal of his own in the second half, with Rooney capping off the victory with his third strike in the 89th minute.
In other results, Liverpool returned to winning form in a 3-1 win over Aston Villa through first half goals from striker Dirk Kuyt, forward Peter Crouch and midfielder Luis Garcia, while Gabriel Agbonlahor netted for Villa in the 56th minute.
Portsmouth also scored a 3-1 victory at Fratton Park over Reading with Royals midfielder Brynjar Gunnarsson putting the ball into his own net to open the scoring in the 10th minute.
Nwanko Kanu and Pedro Mendes added second half goals for the home side, while striker Kevin Doyle scored a late consolation goal for the visitors.
Speaking of late goals, Henri Camara scored in the 83rd minute to give Wigan a 1-0 win over Fulham at Craven Cottage, after Latics midfielder Danny Landzaat missed a penalty in the 75th minute.
Arsenal salvaged a 1-1 draw against Everton after going behind to a Tim Cahill strike in the 11th minute at the Emirates Stadium, with Robin van Persie equalising in the 71st minute for the Gunners.
Watford and Tottenham played out a 0-0 draw at Vicarage Road.