Watford were the only top-flight team to be knocked out in Tuesday's League Cup second-round ties, but Stoke City, West Brom, Aston Villa and Crystal Palace were all given scares by lower-league opposition.
Premier League new boys Watford suffered a 1-0 defeat at Championship side Preston - Marnick Vermijl's early goal settling matters - and also saw Miguel Britos sent off on his debut.
Stoke, who welcomed back Bojan for his first competitive appearance since January, and West Brom required penalties to see off Luton Town and Port Vale following respective 1-1 and 0-0 draws, while Villa and Palace were taken to extra time on home soil by Notts County and Shrewsbury Town.
Villa ultimately ran out 5-3 winners, Scott Sinclair scoring a hat-trick, and Palace cantered home 4-1 to book their place in round three.
Following their dismal start to the Premier League season, Sunderland were grateful for three goals from Jermain Defoe as they ultimately proved too strong for fourth-tier side Exeter City in a nine-goal thriller at the Stadium of Light.
Exeter came from 2-0 and 3-2 down to reach half-time on level terms, before going down 6-3, with Jack Rodwell (2) and Duncan Watmore also on target for Dick Advocaat's men.
Florian Thauvin enjoyed a productive first start for Newcastle United, scoring an early opener and setting up three more in a 4-1 home win over Northampton Town.
Elsewhere, Junior Stanislas scored twice in Bournemouth's 4-0 success at Hartlepool United, debutant Joe Dodoo went one better with a hat-trick as Leicester City triumphed 4-1 at Bury, Norwich City saw off Rotherham United 2-1 and Swansea City eased to a 3-0 home victory over York City.
Reading, Fulham, Hull City, Charlton Athletic, Birmingham City, Sheffield Wednesday and Wolves also booked their places in round three inside 90 minutes, but MK Dons, Ipswich Town and Middlesbrough needed extra-time to see off the respective challenges of Cardiff City, Doncaster Rovers and Burton Albion.
Carlisle United were another team to spring an upset, winning 2-1 at QPR, while Walsall secured victory by the same scoreline at home to Brighton and Hove Albion.
