Watford was the only top-flight team to be knocked out in Tuesday’s League Cup second-round matches, but Stoke City, West Brom, Aston Villa and Crystal Palace were all given scares by lower-league opposition.
Defoe’s treble in a 6-3 win over Exeter compensated for defensive gaffes which allowed the fourth-tier side to draw level at 3-3 at halftime.
Jon Stead’s penalty in first half stoppage-time put County back in front.
In an end-to-end encounter, former Villa man Graham Burke’s superb strike gave the visitors the lead again, before Sinclair’s penalty on 79 minutes forced the game to extra time.
Stoke were pushed to the brink of a shock exit before beating fourth tier Luton 8-7 on penalties after a 1-1 draw at Kenilworth Road.
Defending champions Chelsea will also be playing away to League One side Walsall.
Liverpool will also be playing at home as League Two side Carlisle United travel to Anfield.
Fresh from their first win of the season against West Ham, BOURNEMOUTH saw off HARTLEPOOL 4-0 with goals from Yann Kermorgrant, Dan Gosling and a Junior Stanislas double. Miguel Britos was sent off on his debut for Watford, which is still searching for its first win after returning to the Premier League.
Norwich flop Ricky Van Wolfswinkel scored only his second goal for the Canaries in their 2-1 win at Rotherham.
Palace eventually triumphed 4-1 after an extra 30 minutes having been held 1-1 at home by third-tier Shrewsbury Town. The Red Devils have a 25-18 record (with 9 draws) with the Suffolk based side and the Dutch boss will be looking to improve on last season’s highly criticized 4-0 defeat to MK Dons in the second round.