The Blades' cup performances over the past year have belied their League One status, securing five Premier League scalps and reaching the last-four juncture of last season's FA Cup and now this competition.
United looked like they would once again prove the scourge of top-flight opposition, only for Townsend's second-half penalty to see Tottenham eke out a 1-0 win in north London.
It is a welcome cushion ahead of what is sure to be a combative second leg at Bramall Lane next Wednesday, especially if Clough's men can match this performance.
United started brightly and frustrated Spurs in the first half, showing no ill-effects of the traffic-delayed arrival which saw kick-off put back until 8pm.
An Eric Dier header was the only shot on target either side could manage in a dull opening period, although Emmanuel Adebayor should have tested United goalkeeper Mark Howard as half-time approached.
The Togo striker, captaining the side on his first start since November 2, was perhaps fortunate not to receive a red card before that after catching Louis Reed - and was once again booed by some Spurs fans.
His substitution proved a shrewd move as replacement Roberto Soldado quickly made an impact, with his presence causing Jay McEveley to flap an arm at the ball and referee Neil Swarbrick to point to the spot.
Townsend duly converted the penalty, much to the home faithful's relief, although Mauricio Pochettino will know a much-improved display will be needed in the Steel City if they are to reach the Wembley finale.