Greg Rioch's side took the lead but with a Billy Daniels penalty in the 13th minute on a heavy pitch which was not helped by the drizzle.
Ricky Duncan's side levelled in the 32nd minute when Hicham Abdellah hit a 25 yard shot which flew over Lee Burge and into the top corner of the net.
City, with some good crosses being provided by wingers Josh Ruffles and Luke Bottomer, whilst Conor Thomas looked very comfortable in midfield, had more shots in the first half but in the 64tn minute, a long kick from the home keeper was headed on and the ball went under the foot of Lee Burge and fell for Julian Okai to round the City keeper and tap into an empty net.
Burge could do nothing nine minutes later when a free kick inside the centre circle was pumped forward to Duane Ofori-Acheampong, who scored from twleve yards out with a back header to put the Shrimpers into the Fourth Round where they face a trip to Derby County.
STATS
Corners 1st half Southend 3-2 City 2nd half Southend 3-6 City
Shots On Goal 1st half Southend 6-7 City 2nd half Southend 6-10 City
Att 250 estimate (7 City)
City Man Of The Match - Josh Ruffles followed by Conor Thomas and Luke Bottomer.
City team
Burge, Christie, Willis, Adams, Gudger (Henderson 85), Bottomer (Roberts 83), Grogan (Birgirimana 59), Clark-Harris, Daniels
City U18's are back in action on Saturday with a home game against Cardiff City.