With the game having finished 1-1 after 90 minutes, it was left to the lottery of penalties.
Jamie Shackleton missed Leeds’ vital sudden-death spot-kick when he thumped the bar, after which Salford’s Ossama Ashley notched the winning kick – dramatically at the second attempt after Karl Darlow had moved off his line to save the first.
As expected, with 46 league places between the two teams and visiting boss Daniel Farke going with a strong starting line-up, Leeds bossed the opening half-hour at the Peninsula Stadium.
Crysencio Summerville saw a free-kick saved by Alex Cairns, while Willy Gnonto was denied by Liam Shephard’s smart block.
The woodwork saved Salford when Summerville turned past Stevie Mallan before curling a shot against a post.
Despite Leeds’ dominance, it was Salford who broke the deadlock after 34 minutes. Ex-Leeds youth prospect Luke Garbutt crossed in for former Elland Road striker Matt Smith and he headed powerfully past a stunned Darlow.
Leeds piled the pressure on after the restart. Skipper Pascal Struijk headed straight at Cairns, while Summerville forced the Ammies keeper into another superb save.
Leeds finally struck in the 76th minute. Struijk bundled home from close range after sub Sam Greenwood’s free-kick was not cleared by the Ammies’ overworked defence. The brilliant Cairns later denied £36m man Georginio Rutter, then Greenwood thumped the bar, meaning the game was to be settled in a shoot-out. Rutter and Connor McLennan also failed to score as all 20 outfield players had to step up.
Leeds, meanwhile, are pushing ahead with completing a loan move for Tottenham Hotspur right-sided defender Djed Spence – but one player who will not be joining in the final week of the window is Bayer Leverkusen midfielder Nadiem Amiri.
The Athletic are reporting that the Championship club have ended their interest in the German international, 26, who was flown over to the UK following United's weekend win at Ipswich Town.
A £5million fee had been agreed with the Bundesliga outfit, but after talks on Monday, Leeds officials have elected to abandon their pursuit of the player due to his financial demands.
Meanwhile, ex-Middlesbrough defender Spence is undergoing a medical at Leeds ahead of sealing his switch back to Yorkshire.
The had been linked with numerous other clubs including Bristol City and Swansea City. Leeds are set to pay a £1m loan fee with no buy clause included in the deal.
Salford City: Cairns, Shephard (McLennan 46), Mariappa, Tilt, Bolton, Mallan, Watson, Garbutt (Lund 73), Ashley, Hendry (McAleny 70), Smith (Dackers 88). Unused substitutes: Bailey, Wright, Berkoe, Vassell, Olopade.
Leeds United: Darlow, Shackleton, Cresswell, Struijk, Hjelde, Gray (Greenwood 76), Ampadu, Gnonto, Gelhardt (Sinisterra 61), Summerville, Rutter. Unused substitutes: Meslier, Ayling, Klaesson, Rodon, Gyabi, Bate, Drameh.
Referee: O Langford (W Midlands).