Goalkeeper Aaron Ramsdale was the hero as the Blades progressed to the second round of the FA Youth Cup on Tuesday night.
The teenager saved two spot-kicks and scored another as the Blades booked a date with the winner of the Stourbridge v Chesterfield tie.
Shea Gordon, Callum Semple and Brodie Litchfield also netted from the spot after 120 minutes of Bramall Lane action could not separate the sides.
Good work from skipper Gordon presented the first chance to the Blades on five minutes but Smith's shot was blocked. Gordon also attached himself to a Hallam corner soon after but the header was wide.
Blades goalkeeper Ramsdale made an acrobatic save to keep the scoreline blank on 19 minutes when he flicked away an audacious attempt from Webb-Foster, and the fast and frantic action of the first half failed to produce many other clear cut chances, although both sides looked for openings and won a number of corners.
Gordon shot straight at visiting goalkeeper Sykes-Kenworthy, Litchfield and Hallam were lively in attack in the first period, whilst for Bradford Cissa continually tried to find space.
Bradford made the brighter start to the second half but again chances were limited, the best they could muster early on was a cross from Hudson which Webb-Foster headed wide.
Fans inside the Lane would have wondered how United did not take the lead just after the hour. Goalkeeper Sykes-Kenworthy did well to prevent Omolokun scoring an own goal and then the stopper, with the aid of a post, kept out two close range efforts from Litchfield, who pounced on the rebound.
In the final 15 minutes there was still all to play for. For the Blades, Smith fired straight at the goalkeeper, whilst Bradford's Devine watched his long range effort skim the top of the crossbar.
As the 90-minute mark approached, Kelly put in an inviting cross, Gordon again shot at the goalkeeper and seconds before extra-time, the Blades had a chance to win it. Smith's deep free-kick saw Litchfield head against the back of team-mate Cummings.
The first period of extra time was a cagey affair with both sides determined not to throw the game away, the only effort of note came from United's Litchfield on 95 minutes but he half-volleyed over the crossbar.
United started the second period well, winning two early corners and Brown almost created a chance after robbing Boateng. For Bradford, Powell poked wide and McBurnie clipped into Ramsdale's arms.
Late on there was a chance for both sides. Ramsdale pushed away Hudson's effort from an acute angle and after Slew had been fouled on the edge of the box, defender Semple's free-kick deflected off the wall meaning penalties was required.
Penalties (Blades first)
Gordon - scored - 1-0
Webb-Foster - scored 1-1
Ramsdale - scored - 2-1
Cissa - saved - 2-1
Semple - scored - 3-1
McBurnie - scored - 3-2
Litchfield - scored - 4-2
Devine - saved - 4-2
Blades win 4-2 on penalties
Blades: Ramsdale, Charlesworth, Kelly, Cummings, Semple, Smith (Brown 104), Gordon, Litchfield, Hallam (Maw 57), Mallon (Slew 85), Gilmour.
Unused: Perryman, Ramsey.