Paul McGuinness' side broke through on the quarter-of-an-hour mark when a neat move led to Sam Byrne playing in Pearson, who ran through from midfield to flash home a terrific finish with his right foot.
Derice Richards equalised before the break by sweeping a controlled finish wide of the diving Jonny Sutherland and the Potters were on top in the second half after getting back onto level terms.
A corner from the left caused problems and James Alabi was able to find the net with a header as the hosts failed to clear. Sutherland pulled off a number of fine saves but United were unable to battle back at the other end to earn a point.
United: Sutherland; Grimshaw, McNair, McConnell, Rowley (Pereira 65); Weir, Pearson (Harrop 65), Rothwell, Daehli; Byrne (Love 65), Wilson. Sub not used: Dalley, O'Hara.