New hitman Ched Evans wasn't to be seen, Billy Sharp also didn't feature, but Ryan France and Keith Treacy made their second appearances for the red and white wizards.
The Blades were on the back foot immediately but luckily Fagan's shot was blasted over after a bright opening. Robertson then drilled the ball wide and shortly after Leigh Bromby's header was deflected.
On loan Blackburn winger Keith Treacy pulled some trickery out of the blue, his pitch-perfect back heel found Andy Taylor who could divert the ball towards the back-post to meet Leigh Bromby who netted his third pre-season goal in three pre-season games.
Fagan was positioned beautifully to turn in Clarke's cross but Bromby confidently intercepted. One change was made at the break, the Imps chose to bring on a pair of fresh legs. Lee Hendrie and Jamie Ward went close after Jordan Robertson's forceful crack was blocked.
Leigh Bromby was all over the place, this time back up top when he latched on to Brian Howard's corner to head on to the top of the crossbar. Several substitutions were made in a 10-minute-period by Blackwell, which included Glen Little who recently was offered terms at Bramall Lane.
Clarke blazed Connor's pass over with the Imps searching for an equaliser. Brian Howard wasn't far off target, in fact only a yard or two - a volley by the former Barnsley man skimmed wide.
Academy graduate Phil Roe was awarded a rare senior outing, and then any chance of Lincoln salvaging an equaliser were diminished. Glen Little stepped up to the plate and fired the ball into the corner of the goal.
The Blades have completed their pre-season programme and have a 100% win record. Sheffield United have no pre-season friendlies remaining so the next time they will be vying against opposition will be in 9 days time (7th August) when they face Middlesbrough at The Riverside Stadium. And it must be noted that Boro boss Gareth Southgate was watching Tuesday night's tie at Sincil Bank.