Kit Graham’s extra-time winner saw Tottenham edge out the Blades 2-1 at The Hive.
The hosts went ahead in the 29th minute when Lucy Quinn fired a fierce right-footed shot into the back of the net.
Spurs were unable to hold on though as Neil Redfearn’s United hit back with 10 minutes to go after a defensive mishap allowed Lucy Watson to stroke the ball into an empty net.
That sent the match to extra time, where Graham struck what would prove to be the winner in the 108th minute when she rose highest to head home for Rehanne Skinner’s side.
That goal secured Spurs a place in the last eight of the competition, which is scheduled to take place in September.
Brighton cruised into the quarter-finals with a 6-0 win over third-tier Huddersfield.
The hosts broke the deadlock after 15 minutes when Huddersfield failed to clear a corner and Nora Heroum slotted the ball into the net.
Rianna Jarrett doubled the home side’s lead with a bullet header and an own goal, with the ball appearing to go in off goalkeeper Bethan Davies, made it 3-0 after 33 minutes.
Heroum missed a chance to add to her tally before the break as her penalty was tipped over the crossbar by Davies.
Fliss Gibbons made it 4-0 in the second half before Danique Kerkdijk added a brace to wrap up a comprehensive win for Hope Powell’s Women’s Super League side.
Elsewheere, Arsenal breezed into the quarter-finals with a resounding 9-0 victory over Championship side Crystal Palace.
Gunners captain Kim Little opened the scoring from the penalty spot, Beth Mead doubled the advantage before Danielle Van De Donk then scored from close range moments before half-time.
Noelle Maritz made it four on the hour mark and Jordan Nobbs swept home for 5-0.
Vivianne Miedema headed home a sixth before Jill Roord tapped home on her final appearance.
Maritz completed a brace and Katie McCabe made it eight different goalscorers with a stoppage-time free-kick.
Casey Stoney’s Manchester United reign ended with a 3-2 defeat to Championship winners Leicester at Leigh Sports Village.
Jess King scored Charlton’s goal as they beat Blackburn 1-0, while Sarah Mayling’s strike helped Birmingham beat Southampton 3-2.
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