Craig Reid came closest to breaking the deadlock, hitting the woodwork from long range in the first half.
The second leg is at Bramall Lane on Monday night.
Boro, looking for a third successive promotion having been in the Conference just two years ago, came agonisingly close to grabbing a vital lead when Reid's shot hit the crossbar.
But Danny Wilson's United, pipped by city rivals Wednesday to automatic promotion last weekend, should now be in the driving seat.
However, the Blades' record in the play-offs will not inspire much confidence, with five failures from five attempts, while they have not beaten Stevenage, who finished 17 points behind them, in three matches this season.
And having recently lost top scorer Ched Evans to a jail sentence and James Beattie through suspension, they look desperately short of firepower.
Chris Porter, who has not scored in the league this year, was on his own in attack but he barely had a sniff as Boro bossed the opening stages.
Midfielder Michael Bostwick cleverly weaved his way past a couple of challenges but his attempted curler was way off target, while lively former Arsenal youngster Luke Freeman also fired high and wide.
And four minutes before the break the hosts were inches from going ahead, Reid's dipping 20-yard shot beating Blades goalkeeper Steve Simonsen but not the crossbar.
The visitors were cheered on by their former player, Tottenham and England defender Kyle Walker, who made the short trip from north London to take his place in the away end.
And they responded to almost going behind by finally mustering their first attempts at goal.
Stephen Quinn blazed over after his initial shot was blocked and Kevin McDonald fired wide in first-half stoppage time.
United improved in the second half and Boro keeper Chris Day was eventually called into action after an hour, comfortably dealing with Lee Williamson's low drive from outside the area.
Michael Flynn could have broken the deadlock 10 minutes later when he was put through by Matt Hill, but the winger elected to cut the ball back to no-one and the chance disappeared.
Blades substitute Richard Cresswell had a deflected shot saved by Day and a late header hacked clear.
But neither side looked capable of making the breakthrough, and another nervy affair looks on the cards in three days' time with Wembley just 90 minutes away.
