Brentford suffered the biggest shock of the night on Tuesday, despite taking a third-minute lead through England World Cup hopeful Ivan Toney.
Gillingham had just one shot on target but made it count when Mikael Mandron headed in an equaliser 15 minutes from time.
Mikkel Damsgaard is going to Qatar with Denmark, but he was the only man to miss in a high-quality shootout as the visitors won 6-5 on penalties.
Leicester continued their upturn in form with a 3-0 win over fourth-tier Newport, while Bournemouth humbled Premier League rivals Everton 4-1.
Championship leaders Burnley bounced back from their first defeat in 18 games to Sheffield United on Saturday to beat Crawley 3-1 thanks to two goals from Anass Zaroury.
MK Dons, Lincoln City and Charlton also progressed to the last 16.
Man City take on Chelsea in the pick of Wednesday's ties with holders Liverpool, Arsenal and Tottenham also in action.