The north-east outfit made the long journey to the Essex coast for the tie and it started well for Craig Liddle's side as they surged into a 2-0 lead.
Southend United 3-4 Middlesbrough
The FA Youth Cup
Third Round Proper
Friday 12 December 2014
Roots Hall, Southend
A goal from Harry Chapman in the sixth minute broke the deadlock and the same player added a second soon after to put his side in control.
And England U18s defender Dael Fry then saw a shot hit the post as Boro threatened to run riot over their hosts.
But the Shrimpers hit back when Jordan Williams' mis-hit cross floated in off a post to give themselves hope, and they quickly followed that up with a 39th minute equaliser from Freddie Gard to catch Boro cold.
The second half saw both sides really going for victory and it was Southend who thought they'd edged it when the impressive Nico Cotton crashed home a 20-yard shot in the 89th minute.
Boro were desperate as they threw everything at the young Shrimpers, including Fry being deployed as an additional striker, and it paid off when substitute Jonathan Helm levelled things up in stoppage time.
With extra-time looking to be on the cards, Boro's momentum carried them forward again and when England U18s midfielder Callum Cooke's cross caused confusion in the Southend box, Lee Heatherington rammed the ball home from close range to win it for Boro.
The result means Middlesbrough will now face either Millwall or north-east rivals Newcastle United in the Fourth Round, with those teams due to meet at the Den on Saturday.