Leeds 2-2 Swindon (aet - Leeds win 4-3 on penalties)
Robinson scored with a thunderous header
Keeper Paul Robinson proved the hero for Leeds as they clawed their way into the third round of the Carling Cup on penalties.
Robinson scored an injury-time equaliser for the Elland Road side before making the decisive save in the penalty shoot-out to deny brave Swindon.
The Second Division side looked to be heading for a famous victory when they took a 2-0 lead through Sam Parkin in the 74th minute.
But full-back Ian Harte pulled a goal back for Leeds
minutes later, before Robinson sent a thundering header past his counterpart Rhys Evans in the closing seconds.
Leeds were unable to break down their resolute opponents - who had been reduced to 10 men with the sending off of Bart Griemink moments before Robinson scored - in extra-time.
And it took more heroics from Robinson in the penalty shoot-out to take his side through.
He saved a spot-kick from Stefani
Miglioranzi to keep Leeds level at 3-3 before Swindon skipper Andy Gurney struck his penalty against the post.
Leeds struggled to find any rhythm in the first half and suffered a further setback when skipper
Gary Kelly had to leave the field with concussion after an accidental clash with Parkin.
Kelly's departure led to Lucas Radebe playing in an unaccustomed right-back role and
Alan Smith taking on the captaincy.
And at the end of the half Swindon capitalised. A foul by Leeds midfielder Zoumana Camara on Jon Stevenson resulted in Gurney thundering a 30-yard
free-kick past Robinson.
Didier Domi, on at the break for the ineffective Jason Wilcox, should have
levelled matters within minutes of his introduction, but he skied a close-range
effort over the bar.
In the 74th minute Swindon appeared to have victory wrapped up.
Parkin latched onto a through ball from Sammy Igoe before lofting his shot over the advancing Robinson.
But within three minutes Leeds gave themselves a lifeline with Harte volleying
home from seven yards.
Then came the late drama involving both keepers, with
Robinson emerging with the biggest smile to spare Leeds' blushes.
Leeds: Robinson, Kelly, Camara, Roque Junior, Harte, Lennon, Batty, Olembe, Wilcox, Smith, Chapuis. Subs: Carson, Radebe, Bridges, Seth Johnson, Domi.
Swindon: Griemink, Gurney, Heywood, Reeves, Duke, Hewlett, Miglioranzi, Grant Smith, Igoe, Parkin, Stevenson. Subs: Evans, Viveash, Herring, Nicholas, Howard.
Referee: M Clattenburg (Co Durham).