Lincoln will host Premier League champions Liverpool in the Carabao Cup third round after romping to victory at Bradford.
There were no major upsets as the second round got under way, but a number of clubs set up attractive ties in the next round.
The League One Imps were among them, having thrashed Bradford 5-0 in their second-round tie at Valley Parade.
Luton will host Manchester United after Jordan Clark secured a 1-0 win at Reading, while Barnsley will travel to Chelsea after Patrick Schmidt and Jordan Williams goals saw off Middlesbrough 2-0.
Leyton Orient will host Tottenham after substitute Danny Johnson's last-gasp goal secured a memorable comeback 3-2 win against Plymouth.
Argyle went two up though Panutche Camara and Kelland Watts, only for Jordan Maguire-Drew, Jobi McAnuff and Johnson to turn things around.
Fleetwood are through to the third round for the first time after a 2-1 win against Port Vale.
Jack Grealish celebrated his new five-year deal by scoring as Aston Villa, last season's Carabao Cup runners-up, emerged 3-1 victors at Burton.
Holders Manchester City will face Bournemouth after the relegated Cherries won a mammoth penalty shootout against Crystal Palace after the match ended 0-0.
Debutant Ryan Fraser's goal edged Newcastle past Blackburn 1-0 and secured a trip to Morecambe, who won by the same scoreline thanks to Aaron Wildig's goal against Oldham.
Under-fire West Ham cruised through to the third round with a 3-0 win against Charlton as Felipe Anderson added to Sebastien Haller's brace.
Gary Rowett's Millwall will host Burnley or Sheffield United after they beat Cheltenham 3-1, with Ryan Leonard, Connor Mahoney and Matt Smith scoring before Finn Azaz's consolation effort.
Gillingham are heading to Wolves or Stoke after beating Coventry on penalties while Derby bowed out after blowing a home lead against Preston in a 2-1 loss.
Newport overcame Cambridge 1-0 thanks to Scott Twine's late goal and will face Watford, who beat Oxford on penalties thanks to Daniel Bachmann's heroics.
Elias Kachunga and Josh Windass secured Sheffield Wednesday's place in the third round with a 2-0 win at Rochdale.