Travis Binnion's side went into the meeting on a run of four consecutive league wins, and made it five thanks to strikes from Malachi Sharpe in the first period and Jack Moorhouse in the second.
Meanwhile, at the other end, Reds goalkeeper Elyh Harrison prevented Spurs getting on the scoresheet with several saves, including one to deny Ellis Lehane in stoppage time.
Sharpe's opener came in the 37th minute and was set up by Chido Obi - who used to play youth football for Spurs' great rivals in north London, Arsenal.
Jack Moorhouse doubled United's lead in the 73rd minute; this time, left-back Harry Amass was credited with the assist.
Both of the Reds' scorers also found the net in last week's 5-0 win over Oldham Athletic in the National League Cup.