Canaries top scorer Grant Holt grabbed his 17th goal of the season in the 68th minute to break the deadlock in Tuesday night's League One clash.
The City skipper fired into the bottom right-hand corner of Steve Mildenhall's goal after Wes Hoolahan's cross from the left was missed by Sean Morrison and tapped into the striker's path by Korey Smith.
And Smith secured the points for high-flying Norwich in the 77th minute when he latched onto Chris Martin's centre and saw his right-foot shot deflected in off Scott Malone.
Southend had the ball in the net on 88 minutes but Jabo Ibehre's header from a Simon Francis cross was ruled out for handball by the striker, who was making his debut on loan from MK Dons.
Holt made it 18 goals from the penalty spot in stoppage time after Alan McCormack brought down substitute Luke Daley.
Holt fired low into the left-hand corner of the net with Mildenhall diving the wrong way.