The 21-year-old twice foiled Michael Tonge as Andy Hessenthaler’s side proved again they will be one of the most difficult sides to beat in Nationwide Division One.
Gillingham, without Marlon King, Rod Wallace and skipper Paul Smith, went close in the ninth minute, full back John Hills curling a free kick over the wall, the ball spinning the wrong side of the bar.
United squandered a chance minutes late as Tonge found space on the left flank. His low cross evaded a packed goalmouth and Wayne Allison steamed in at the far post but hammered the ball high over the target from ten yards.
Jack Lester, signed on a free from Forest last month, was given a half-chance in the 26th minute, as he twisted with his back to goal to unleash a low left-foot shot that was snatched on the line by Brown.
Gillingham got round the back of the Blades back four, Nicky Southall threading the ball to the darting Danny Spiller who pulled the ball across the face of the United goal, Peter Ndlovu clearing with Mamady Sidibe waiting to pounce.
Brown foiled United again in the 39th minute after Ndlovu’s darting run took him across the face of the Gillingham area.
His deep cross was aimed at Allison lurking at the far post, the ball was cleared to Tonge unmarked on the edge of the box and his low strike was snatched by the diving Brown.
Centre back Chris Morgan, one of eight new signings by United manager Neil Warnock, should have broken the deadlock in first-half injury time as he rose to meet a Tonge cross from the right but screwed his header wide of the far post from six yards.
Brown then saved bravely at the feet of Allison after smart work by Michael Brown and in the dying minutes he jumped to his left to produce another eye-catching stop to keep out Tonge's long-range effort.