Republic of Ireland Under-21 internationals Festy Ebosele and Louie Watson both impressed as Derby survived a Carabao Cup scare before beating Salford 5-3 in a penalty shoot-out at Pride Park.
Watson netted the winning shoot-out penalty, while former Bray Wanderers player Ebosele was named the man-of-the-match on what was his first senior start for the club.
Derby were behind after eight minutes when Jordan Turnbull headed in after Ashley Eastham flicked on a corner.
Salford scored again in the 14th minute when Josh Morris beat Allsop with a 20-yard shot that curled just inside his right-hand post.
Allsop saved from Conor McAleny but Derby pulled a goal back four minutes later when Isaac Hutchinson turned inside the box to fire low past Tom King.
Derby were much better in the second half and levelled in the 70th minute when Josh Lowe tripped Ebosele and Colin Kazim-Richards scored the penalty despite slipping as he ran up.
But Salford regained the lead four minutes later when Burgess was barged over by Craig Forsyth and Morris dispatched the penalty.
Derby equalised in the 82nd minute when Morrison fired into the top-left corner after his free-kick came back off the wall.
Fellow Championship side Blackburn were not so fortunate and suffered a 2-1 loss to Morecambe on the same day they sold forward Adam Armstrong to Southampton.
Tyrhys Dolan put Rovers ahead in the first half but goals from Cole Stockton and Adam Phillips at Ewood Park gave Stephen Robinson his first win in charge of the League One Shrimps.
Barnsley, who lost in the play-offs last season, were knocked out after a 6-5 loss on penalties at Bolton. Joel Dixon denied Devante Cole from 12 yards after the tie had ended goalless.
Stevenage goalkeeper Joseph Anang made two saves in the shootout as the League Two outfit beat local rivals Luton 3-0 on penalties after a 2-2 draw.
Another Championship side lost on spot-kicks to lower opposition as Hull were beaten by League One Wigan.
After 14 successful penalties, Manchester United loanee Di'Shon Bernard missed and Jordan Cousins secured the Latics an 8-7 victory after the contest had finished 1-1.
Bristol City were another Championship side to taste defeat. Forest Green's Regan Hendry netted in the sixth minute of stoppage-time to force penalties, which they won 6-5 to knock the Robins out.
Sutton's first EFL Cup tie ended in a 3-2 defeat at Championship Cardiff after they had taken an early lead through Donovan Wilson with Marley Watkins' double and Josh Murphy doing the damage despite Coby Rowe's late strike.
Ryan Hardie hit a double for Plymouth in a 4-0 thrashing at newly promoted Peterborough.
Rhian Brewster ended his long wait for a first Sheffield United goal with the winner in a 1-0 victory over Carlisle while Stoke beat Fleetwood 2-1.
Swansea eased past Reading 3-0 and Scott Sinclair scored twice as Preston beat Mansfield by the same score.
Jobe Bellingham, the younger brother of England international Jude Bellingham, was an unused substitute during Birmingham's 1-0 win over Colchester.
Aged only 15-years-old, the academy star would have broken his sibling's record as the club's youngest player if he entered the pitch but Lee Bowyer had to wait until the 75th minute for Marcel Oakley to break the deadlock on his debut and send Blues into the next round.
Millwall responded to going behind early to see off Portsmouth 2-1 while AFC Wimbledon beat Charlton 1-0.
Shrewsbury needed penalties to beat Lincoln while Colby Bishop scored four minutes from time to earn Accrington a 2-1 triumph at Rotherham.
Cheltenham edged a West County derby with Bristol Rovers 2-1, while Doncaster needed penalties to beat Walsall after a 0-0 draw.
Gillingham beat Crawley 10-9 on spot-kicks and Wycombe goalkeeper David Stockdale saved three penalties and scored one in their shootout success victory at Exeter.
There were also triumphs for Crewe, Cambridge, Newport, Oldham and Barrow at the expense of Hartlepool, Swindon, Ipswich, Tranmere and Scunthorpe, while Rochdale were handed a bye due to an outbreak of coronavirus at opponents Harrogate.