United had taken the lead through young starlet Che Adams before a Amari Morgan-Smith strike levelled for the hosts. But back to back goals for Higdon and Baxter in the 89th and 90th minute respectively was enough to ensure a second pre-season victory for new boss Nigel Adkins.
In contrast to the win at Ilkeston last Saturday the Blades chief opted to field a starting XI, all of which played 60 minutes before changing personnel. The replacements included a debut for Martyn Woolford and the inclusion of Jamie Murphy.
From the off it was evident that Adams would be installed as striker and this tactical moved paid off, within 13 minutes a cool ball through from Dominic Calvert-Lewin saw ADAMS fire past Phillips in the Robins goal; 1-0.
The hosts were reduced to set pieces as they struggled to carve their way through the United defence but came close when Storer hit wide, Pell fired over the bar and Parslow saw his header off target. Close to the break Calvert-Lewin almost turned home from a James Wallace free-kick. Before the half-time whistle blew there was further action to be had, McGahey's clearance was intercepted by Munns and his ball through to a unmarked MORGAN-SMITH who fired home from distance past Long.
Early in the second half Conor Dimaio and Diego DeGiralomo made attempts to get back into the lead but failed before Long was forced into action, saving Downes effort before - on the hour mark - the subsequent changes were made.
Higdon was unfortunate to not get on the score-sheet in the win at Ilkeston after he saw two efforts cleared off the line and it seemed as though he would get short change at Whaddon Road also as he headed Campbell-Ryce's cross into the arms of substitute Kitscha. At the other end Dale created a shot and fired wide.
With the two teams fielding a new XI they both struggled to find shape within the team and came as no surprise that the goal mouth action was somewhat drab from then onwards, right until the closing minutes when the 236 travelling Blades fans were treated to some celebrations. Woolford's corner was attempted to be cleared but HIGDON collected on the edge of the box and his half-volley cannoned into the back of the net.
There was enough time for the visitors to claim a third goal before the end of the game, Murphy proved the catalyst down the left flank and his low cross fell kindly for BAXTER to hit home; 3-1.
Cheltenham Town: Phillips, McLennan, Storer, Downes, Barthram, Pell, Wright, Morgan-Smith, Waters, Munns, Parslow. Subs: Kitscha, Bowen, Williams, Deaman, Dale, Kotwica, Wynter, Hall, Rowe.
Sheffield United: Long (Howard 60), Dimaio (Freeman 60), McGahey (Collins 60), K. Wallace (McEveley 60), McFadzean (Woolford 60), Scougall (Campbell-Ryce 60), J. Wallace (Basham 60), Reed (Baxter 60), Calvert-Lewin (Murphy 60), Di Girolamo (Higdon 60), Adams (McNulty 60).
Attendance: 1,247