But Henderson latched on to a pass from Stephen Quinn and added to his two first-half strikes with a cool finish across Dean Gerken.
Louis Carey grabbed the other goal for the home side just after the break.
City employed a 4-3-3 formation with Evander Sno moving forward to support Danny Haynes and Nicky Maynard in attack while Lee Johnson was brought in to replace Lewin Nyatanga.
Deadline-day loan signing Carl Ikeme came straight into the United team replacing Mark Bunn in goal while fellow loanee Toni Kallio missed out due to the Blades being up to their maximum quota of five loan player the 18-man squad.
Nick Montgomery returned to the midfield after injury while Henderson came in to the team to lead the line on his own with Ched Evans and Henri Camara missing out.
It was the visitors who had the first real chance on goal after 18 minutes as Quinn found Jamie Ward who hit a shot from the edge of the box which was saved by Gerken.
Gerken was beaten though 14 minutes later as the Blades took the lead in controversial fashion. Henderson received Matthew Kilgallon's cross and beat the keeper from 18 yards but the linesman had raised his flag because Lee Williamson was offside.
Referee Andy Hall however consulted with his assistant and the goal was eventually given prompting a furious response from the City players with Johnson booked for his protests.
Just three minutes later United and Henderson doubled their tally but there were to be no arguments this time.
Ward capitalised on a mistake from Jamie McCombe and slid the ball to Henderson who coolly slotted past Gerken from the centre of the area to put United in total control.
The Robins had not been beaten at home since a loss to Burnley on December 20 last year and they had two good chances to get them back into this contest in the closing stages of the first half.
Marvin Elliott brought a good save from Ikeme from distance before Haynes missed his side's best chance of the half as he put Jamie McAllister's pass into the side netting from six yards.
City got a goal back six minutes after the break as Paul Hartley crossed a free kick into the box and Carey powered home a header from six yards.
And Maynard should have levelled things up for the revitalised Robins with a one-on-one opportunity but Ikeme made a smart save.
Gary Johnson's men had their tails up now and Ikeme was made to work again in the 67th minute as Carey galloped down the left flank and found Haynes who tested the keeper from 20 yards.
City continued to control possession and were eventually rewarded when Saborio beat Ikeme from 12 yards deep into injury time but it was the Blades who snatched all three points with Henderson's late show.