The Black Cats fielded a strong line-up but conceded three times in the first half as their defence was frequently exposed again, before they ultimately rallied to break the visitors’ spirit in the second period.
The hosts were 2-0 up through Jack Rodwell and Defoe before Emmanuel Oyeleke and David Wheeler brought the Grecians back into the match.
Defoe’s second was cancelled out by Tom McCready prior to half-time, yet Rodwell headed in another, Duncan Watmore tapped in and Defoe swept home a third late on.
Watford were a top-flight casualty, though, as they slipped to a 1-0 loss at Championship Preston thanks to Marnick Vermijl’s first goal for North End.
Teenage striker Joe Dodoo also netted a treble while Andrej Kramaric was on target too as Leicester progressed courtesy of a 4-1 win at Bury, for whom Danny Mayor scored.
Bournemouth and Newcastle both struck four in convincing victories over Hartlepool and Northampton respectively. Junior Stanislas claimed a brace while Yann Kermorgant and Dan Gosling each scored in the first half of the Cherries’ 4-0 success.
Florian Thauvin opened his Newcastle account on his full debut, with Siem De Jong, Daryl Janmaat and Mike Williamson also finding the net against the Cobblers, for whom Marc Richards scored a penalty in a 4-1 loss.
Ricky van Wolfswinkel’s first Norwich goal in two years followed Jonny Howson’s first-half effort, before Paul Green pulled one back, as the Canaries saw off Rotherham 2-1. Nathan Dyer, Matt Grimes and Marvin Emnes found the net for Swansea in a 3-0 triumph over York.
Carlisle’s long trip to QPR resulted in a 2-1 success for the visitors thanks to Jason Kennedy’s winner 11 minutes from time after Derek Asamoah and Jay Emmanuel-Thomas traded goals.
Arsenal will travel to Tottenham in the third round, Man United will face Ipswich and Liverpool will play Carlisle.
Birmingham City 2 Gillingham 0, Burton Albion 1 Middlesbrough 2, Bury 1 Leicester City 4, Crystal Palace 4 Shrewsbury Town 1, Doncaster Rovers1 Ipswich Town 4 , Fulham 3 Sheffield United 0, Hartlepool United 0 Bournemouth 4, Hull City 1 Rochdale 0, Luton Town 1 Stoke 1 (Stoke win 8-7 on penalties), Newcastle United 4 Northampton Town 1, Peterborough United 1 Charlton 4, Portsmouth 1 Reading 2, Preston 1 Watford 0, QPR 1 Carlisle United 2, Rotherham United 1 Norwich City 2, Sheffield Wednesday 1 Oxford United 0, Sunderland 6 Exeter City 3, Swansea City 3 York City 0, Walsall 2 Brighton 1, Wolves 2 Barnet 1, Aston Villa 5 Notts County 3, MK Dons 2 Cardiff City 1, West Brom 0 Port Vale (West Brom win 5-3 on penalties).
Dinamo Zagreb 4 Skenderbeu 1 (Dinamo Zagreb win 6-2 on agg), Maccabi Tel Aviv 1 Basle 1 (Maccabi Tel Aviv win on away goals after 3-3 draw on agg), Malmo 2 Celtic 0 (Malmo win 4-3 on agg), Monaco 2 Valencia 1 (Valencia win 4-3 on agg), Shakhtar Donetsk 2 Rapid Vienna 2 (Shakhtar Donetsk win 3-2 on agg).