Newly-promoted County, League Two play-off final winners over Salford in May, led through Callum Roberts at half-time before Zian Flemming equalised early in the second period for the Clarets.
Walker struck the winning penalty after Burnley goalkeeper Max Weiss had saved efforts from Notts pair Emile Acquah and Jacob Bedeau in the shoot-out.
West Ham came from behind to beat Portsmouth 3-1 at the London Stadium in their first match following relegation from the Premier League.
The Hammers fell behind to Adrian Segecic’s first-half opener, but turned it round before the break with Taty Castellanos and Jarrod Bowen on target, before the former notched his second in the second half.
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Substitute Jamal Lowe struck the only goal as Sheffield Wednesday beat 10-man Bolton 1-0 at Hillsborough.
Lowe scored midway through the second half after Bolton's Xavier Simons was sent off for punching Owls' on-loan Leeds striker Harry Gray in retaliation having been pulled back.
Millwall goalkeeper Lukas Jensen saved all four of QPR's penalties as the Lions won 2-0 in a shoot-out at Loftus Road after the game ended 1-1 after 90 minutes.
Luke Cundle had given Millwall a second-half lead before the Hoops hit back through a late own goal from Mark Sykes.
Norwich debutant Andre Brooks was on target as the Canaries cruised to a 4-1 win against MK Dons at Carrow Road.
Cardiff substitute Jack Moylan also scored on his debut, firing the winner as the Bluebirds won 3-2 against Swindon, for whom James Debayo was sent off for two yellow cards in the final six minutes.
August Priske's first-half finish sealed Birmingham a 1-0 win at Swansea and Marc Bola's stunning long-range strike deep in added time clinched Watford victory over Crawley by the same score.
Late goals from substitutes Andri Gudjohnsen and Jayden Fevrier secured Blackburn a 2-1 win at Burton.
Newly-promoted Lincoln picked up where they left off last season, winning 2-1 at Derby thanks to first-half goals from Ben House and Dom Jefferies before Sammie Szmodics pulled one back for the Rams.
Ollie Norburn's own goal and Robert Bozenik's late effort secured Stoke a 2-0 win against Oldham at the bet365 Stadium and Bradford pair Will Swan and Aden Baldwin earned their side a 2-0 home win against Rochdale.
Fleetwood captain Ched Evans' first-half effort sealed his side a 1-0 home win against Chesterfield and Cambridge hit back to beat Barnet 2-1 through second-half goals from Ben Knight and Isaac Heath.
AFC Wimbledon, Barnsley and Reading progressed after winning on penalties against Newport, Wigan and Bromley respectively, while Preston, Shrewsbury and Doncaster came through respective shoot-outs against Huddersfield, Salford and Stockport.
Luca Moore's late goal sealed Crewe a 2-1 victory against Accrington at Gresty Road and late goals from Demetri Mitchell and Idris El Mizouni secured Leyton Orient a 2-0 home win against Oxford.
Peterborough, Luton and Blackpool all won on the road, at Bristol Rovers, Gillingham and Grimsby respectively, and Caleb Okoli's header secured Leicester a 1-0 home win against Northampton.
When is the second round draw?
The draw for the second round of the 2026/27 Carabao Cup will be made live on Sky Sports Football on Monday August 10, during the build-up to the tie between Plymouth and Exeter.
The draw will feature all first-round winners, as well as the 11 Premier League clubs not participating in European competition.
All Saturday's results
- Cambridge 2-1 Barnet
- QPR 1-1 Millwall (0-2 pens)
- AFC Wimbledon 1-1 Newport (5-4 pens)
- Barnsley 1-1 Wigan (6-5 pens)
- Bradford 2-0 Rochdale
- Bristol Rovers 0-1 Peterborough
- Bromley 1-1 Reading (4-5 pens)
- Burnley 1-1 Notts County (4-3 pens)
- Burton 1-2 Blackburn
- Cardiff 3-2 Swindon
- Crewe 2-1 Accrington
- Derby 1-2 Lincoln
- Fleetwood 1-0 Chesterfield
- Gillingham 1-3 Blackpool
- Leicester 1-0 Northampton
- Leyton Orient 2-0 Oxford
- Norwich 4-1 MK Dons
- Preston 1-1 Huddersfield (4-3 pens)
- Salford 1-1 Shrewsbury (3-4 pens)
- Sheff Wed 1-0 Bolton
- Stockport 1-1 Doncaster (4-5 pens)
- Stoke 2-0 Oldham
- Swansea 0-1 Birmingham
- Watford 1-0 Crawley
- West Ham 3-1 Portsmouth
- Cheltenham vs Charlton
- Colchester vs Southampton
- Rotherham vs West Brom
