The home defence looked flimsy from long balls and was equally inept at picking up runners from deep as Telford enjoyed decent spells of possession.
But the Midlanders found Southend goalkeeper Steve Mildenhall in good form and were then undone by Simon Francis' close-range strike and James Walker's excellent curling effort.
Telford had a great chance to take the lead midway through the first half when Andy Brown went through one-on-one, only for Mildenhall to race out to close down the angle quickly and make the block as the shot came in.
Martyn Naylor was then left completely unmarked by the Southend defence, but sliced his shot horribly wide of the post.
Telford continued to create the best opportunities and Mildenhall was forced to make a great save low to his right to keep out Lee Moore's shot, then moments later produced an even better effort to deny the Telford striker once again.
But having ridden their luck for three-quarters of the game, the Essex side grabbed the lead in somewhat fortuitous circumstances.
Telford goalkeeper Ryan Young claimed he was fouled when coming to collect Kevin Betsy's corner, but the referee ignored his appeals as Francis poked the ball home at the far post.
It was perhaps cruel on the visitors and Walker then put the game beyond doubt on 79 minutes, when he cut inside and curled his shot into the top corner.
Telford's heads perhaps understandably dropped and Southend were able to cruise in the final ten minutes to set up a home game against either Altrincham or Luton Town in the next round.