McLeod gave MK Dons the perfect start when he scored his ninth goal of the season from the penalty spot after 16 minutes.
He was released after a fine run down the left by Stephen Quinn, but after beating Shrimpers defender Spencer Prior, he was brought down by the centre-half.
Referee Kevin Wright pointed straight at the spot and McLeod hit the penalty low to the left as Darryl Flahavan dived the wrong way.
Southend struggled to create chances but finally got on terms after 58 minutes through 10-goal leading scorer Freddy Eastwood.
The striker, who bagged 25 goals for Southend last term, picked up a Che Wilson throw and shot straight at Matt Baker from 25 yards, but the ball bounced in front of the keeper, hit his leg and ricocheted into the roof of the net.
Two minutes later winger Mark Gower headed over as the goal sparked the Blues to life.
The winger then hit Baker's right upright after Southend skipper Kevin Maher scuffed his shot.
But hopes that the resurgence would end the League One pacesetter's three-game run without a win were dashed when the Dons regained the lead.
Manager Danny Wilson brought midfielder Smith on for Gareth Edds on 70 minutes and within 60 seconds the substitute restored the lead.
He disposed Gower on the left and then beat three men before firing home under a diving Flahavan in front of the travelling fans.
Southend manager Steve Tilson brought on Mitchell Cole and former MK Dons striker Wayne Gray after 81 minutes in a bid to find an equaliser.
And it looked like his plan had worked a minute from time when midfielder Jay Smith picked out the six-goal forward who beat Baker but then saw his shot cleared off the line by fit-again skipper Ben Chorley.
The visitors held out for three minutes of stoppage time to secure their place in the third round and make it five wins in six matches.