Numerous Premier League sides were in action on Tuesday evening, with more playing on Wednesday.
Aston Villa, Watford, West Ham, Brighton and Southampton secured their places in the third round draw.
However, Norwich were stunned at Crawley Town with the Premier League side losing 1-0.
Elsewhere, Crystal Palace lost on penalties against Colchester, while Stoke beat Leeds on spot kicks.
More Premier League sides are in action on Wednesday.
Everton travel to Lincoln, Burnley host Sunderland, Bournemouth welcome Forest Green and Leicester travel to Burnley.
The Premier League big boys will be in the third round draw, with the likes of Manchester United, Liverpool and Arsenal entering the pot.
All English teams involved in European competition enter at this stage as to not interfere with their continental commitments.
Those concerned this year are Arsenal, Chelsea, Liverpool, Manchester City, Manchester United, Tottenham and Wolves.
The Carabao Cup third round draw will take place on Wednesday evening at around 10pm.
You can watch the draw live on Sky Sports Main Event and Sky Sports Football following the Lincoln vs Everton tie.
The third-round fixtures will take place on September 24 and 25.
Carabao Cup second round results:
Crewe 1-6 Aston Villa
Leeds 2-2 Stoke (Stoke win on pens)
Sheffield United 2-1 Blackburn
Burton Albion 4-0 Morecambe
Nottingham Forest 2-0 Derby
Grimsby Town A-A Macclesfield
Preston 2-2 Hull City (Preston win on pens)
Rochdale 2-1 Carlisle
Rotherham v Sheffield Wednesday
Newcastle v Leicester
Lincoln v Everton
Burnley v Sunderland
Plymouth 2-4 Reading
Crawley Town 1-0 Norwich City
Newport 0-2 West Ham
Oxford United 0-1 Millwall
Watford 3-0 Coventry
Cardiff 0-3 Luton
Bristol Rovers 1-2 Brighton
Crystal Palace 0-0 Colchester (Colchester win on pens)
Fulham 0-1 Southampton
Southend 1-4 MK Dons
Swansea v Cambridge
Bournemouth v Forest Green