After defeats to lower division Bradford City and Doncaster Rovers in the previous two seasons the Whites avoided an unwanted hat-trick with a 5-4 shoot-out success after drawing 2-2 in 120 minutes of cup football.
Leeds looked to be heading out after trailing to an early goal, but Marcus Antonsson’s first goal for the club saved them a minute from time.
Extra-time brought more twists with Chris Wood’s penalty putting United ahead only for Fleetwood to hit back to force a shoot-out that the Whites won thanks to Rob Green making the only save.
They will now face an away trip to Luton Town, who knocked Aston Villa out, in the second round.
Head coach Garry Monk reacted to Sunday’s opening defeat by making five changes with new signing Pablo Hernandez handed his debut and winger Hadi Sacko his first start. Liam Cooper was back in defence, with captain Sol Bamba left out, while Lewis Coyle came in right-back for the injured Gaetano Berardi and Kalvin Phillips partnered Ronaldo Vieira in a youthful central midfield.
If Monk was hoping for an instant reaction to events at Loftus Road he was to be mistaken as Fleetwood went ahead within 13 minutes.
As at QPR the goal again came from a corner that was not dealt with as Aaron Holloway netted from close range.
Sacko and Hernandez were lively early on with the latter having a half-chance only to fire over from inside the area and several dangerous moments being defended well by the hosts.
Another corner brought another chance for Holloway, but this time Kyle Bartley was on the line to clear.
At the other end home keeper Chris Neal was forced to make his first save to deny Kemar Roofe, tipping his half-volley wide.
Leeds were relieved to see Eggert Jonsson’s header go wide, but they finished the half the stronger with Roofe’s 20-yard shot well saved by Neal.
The second half saw Bamba on for Cooper, who has struggled with injury in pre-season, and the first chance fell to United, but Wood headed over from Charlie Taylor’s cross.
Roofe fired a free-kick over and was involved again when he sent over a fine cross that was met by Sacko only for the winger to shoot over.
Fleetwood substitute Ash Hunter was quickly involved as he sent a shot over the bar.
Monk threw Alex Mowatt on for Sacko and Leeds managed a couple of efforts with Roofe making space on the edge of the box before shooting just wide and Wood turning Taylor’s cross over.
On 75 minutes Antonsson became United’s third and final sub as they went for broke in a bid to get an equaliser. They looked set to score five minutes later, but Neal pulled off a superb save to keep out Hernandez’s shot.
It looked like it was not going to be Leeds’ night when Wood sliced a shot wide, but in the 89th minute Antonsson turned well to make space and fired a shot that finally saw Neal beaten.
One more chance was forthcoming with Mowatt seeing a header tipped over the bar and the tie went into extra-time.
Leeds went in front four minutes in when Antonsson was pulled down by keeper Neal and a penalty was the result. Neal was only booked, but could not keep out Wood’s spot kick.
Roofe looked to seal the tie soon after when doing well to get clear before shooting off target from a difficult angle.
However, six minutes into the second half of extra-time Leeds conceded again with Hunter shooting low past Rob Green.
United looked to respond, but Mowatt hit his shot over after working his way into the box.
The last chance went to the hosts, but Bartley made a great block to ensure the tie would go to penalties.
Wood, Antonsson, Mowatt, Phillips and Hernandez then put away their spot kicks for Leeds and although Fleetwood scored their first four, Green saved the last one from Jonsson to guarantee his side’s progress.
Fleetwood Town 2
(Holloway 13, Hunter 111)
Leeds United 2
(Antonsson 89, Wood 94, pen)
Leeds won 5-4 on penalties
Wednesday, August 10, 2016
Fleetwood: Neal, McLaughlin, Bell, Jonsson, Eastham, Ryan, Amadi-Holloway (Hunter 60), Ball (Grant 72), Bolger, Nirennold, Cole (Pond 82).
Leeds: Green, Coyle, Bartley, Cooper (Bamba 45), Taylor, Phillips, Vieira (Antonsson 75), Hernandez, Sacko (Mowatt 65), Roofe, Wood.
Referee: David Coote.