After being pegged back by Michael McIndoe’s last-gasp extra-time spot-kick, Stuart Pearce’s side suffered three successful failures of their own in the decisive duel.
There was no sign of the drama to come in an uneventful opening 90 minutes and it was one of the new boys who on show, young midfielder Stephen Ireland, who created the first chance with a forceful run to the edge of Doncaster’s box.
Having made the hard yards, Ireland had the presence of mind to feed Antoine Sibierski, whose shot was blocked by Warrington.
Sun Jihai passed up the best chance of the match, striding on to Lee Croft’s ball completely unmarked but then blasting against the bar.
The game came to life in extra-time with two penalties and a sending off.
The partisan crowd erupted in anger when referee Graham Salisbury pointed to the spot when Richard Dunne’s surge into the area was ended by Phil McGuire’s shove.
Vassell strode up and smashed the penalty home.
A minute before the end of the first period, Nedum Onuoha slid in on keeper Warrington inside Doncaster’s area, the contact appeared accidental.
Salisbury thought otherwise and immediately brandished a red card. Whatever the rights and wrongs of that decision, Warrington was carried off with a suspected broken leg.
Through sheer numbers being pushed forward, a chance seemed destined to arrive at some stage for Doncaster. But it eventually required another dramatic intervention from Salisbury, who once more pointed to the spot after City skipper Sylvain Distin had handled.
Michael McIndoe wasted no time in rattling home the equaliser.
In the shoot-out, stand-in keeper Jan Budtz was the Rovers hero, saving from Sibierski and Dunne after Vassell hit the bar with his first kick, while McIndoe, Coppinger and Paul Heffernan all scored to take the hosts through.
Brian McBride pounced in the dying moments of extra-time for Fulham to advance after a night of high drama at Craven Cottage.
Fulham were cruising after Zesh Rehman and Heidar Helguson pounced in the space of four first-half minutes but Lincoln staged a stirring second-half fightback.
Francis Green slashed the deficit and a bizarre Moritz Volz own-goal, combined with a string of magnificent saves from goalkeeper Alan Marriott sent the game into extra-time.
Quickfire goals from Liam Rosenior and Tomasz Radzinski appeared to have buried Lincoln’s brave challenge but Scott Kerr and Marvin Robinson then scored to bring the game to 4-4, only for McBride to pounce.
Craig Bellamy hit a brace and Zurab Khizanishvili also scored his first for Blackburn as Rovers saw-off the challenge of Huddersfield Town 3-1 at Ewood Park.
Bellamy found the net for the first time since his £5million summer signing from Newcastle in the 11th minute and Georgian defender Khizanishvili, on a season-long loan deal from Rangers added another on the hour mark.
Huddersfield’s Pawel Abbott hit his ninth goal of the season with 10 minutes remaining but Bellamy added another just five minutes later.
: Warrington (Budtz 110), McGuire, Stephen Roberts, Albrighton, McDaid, Coppinger, Predic (Ravenhill 52), Green, McIndoe, Fortune-West, Guy (Heffernan 81).
: James, Onuoha, Distin, Dunne, Thatcher, Jihai, Reyna (Jordan 90), Ireland, Hussein (Croft 65), Sibierski, Vassell.
: G Salisbury (Lancashire)
* Celtic needed an extra-time goal from John Hartson to overcome a plucky Falkirk side 2-1 at Parkhead last night in the CIS Cup.
Alan Gow gave Falkirk the lead in the 58th minute before Polish international Maciej Zurawski equalised four minutes later to take the game to extra-time.
In the other two games, league leaders Hearts bowed out, going down by the only goal of the game, scored by Ramon Pareira at Livingston, while their Edinburgh neighbours Hibernian are through after seeing off Ayr United 2-1.