After an encouraging start, it was the home side that opened the scoring.
A well crafted training exercise after just six minutes saw Fleetwood set up trialist Lawson D’Ath.
The former Reading and Cheltenham Town loanee struck the ball all from 30 yards that gave Swindon keeper Wes Foderingham no chance.
Three minutes later and the League One visitors responded well as striker Michael Smith had a shot blocked from 25 yards out.
Another Eastleigh trialist, former Bristol City winger Marlon Jackson, won a free kick just outside the box that left back Michael Green take a speculative effort only to find the Swindon wall.
With a quarter of an hour played, Fleetwood was behind another Spitfires attack as the winger linked up with Jack Midson only for Foderingham to gather comfortably.
Moments later, Jackson done well to take it round Ben Gladwin in the right wing after good link up play with Midson however his low cross was cleared away.
Gladwin had a chance himself after 23 minutes but Eastleigh’s Ross Flitney was on hand to save it.
After a quick cooling break, goalscorer D’Ath was replaced by Ben Wright after a half hour.
Midson and Jackson both had further chances in the first half but Richard Hill’s men went into the break with a goal advantage.
Eastleigh started the first half like they finished the first as Wright came close to doubling the home side’s lead.Minutes later, Constable wasted a good chance as the striker could not find Jai Reason with the pass.
Ten minutes into the second half, and Reason sent a poor back pass that led to a Swindon corner.
Green counter attacked on a even poorer corner and set up Wright who couldn’t quite convert after great keeping by Foderingham.
Midson narrowly missed just after the hour mark after Reason whipped in a free kick only for the striker to have his shot deflected for a corner.
At the other end, right back Nathan Thompson sent a low drive hitting the post with 20 minutes to go.
A poor goal kick from Ross Flitney resulted in second half Swindon substitute George Baker firing wide.
Flitney made a close range save from second half substitute Connor Waldron’s shot as Odubade counter attacked at the other end with a speculative shot.
Chances fell for Swindon’s Matt Jones and Will Randall in the last ten minutes but it did not fall their way on the night.
Odubade had a great chance to double the hosts lead in the closing minutes however Swindon’s Lee Marshall was on hand to clear it off the line after the winger done so well.
The Spitfires finally doubled their well earned lead when Odubade swung in a dangerous cross for player/assistant manager McAllister to head home powerfully with almost the last play of the game.
A solid Eastleigh defence made up the two league difference of the two teams on a night that was more than a pleasing workout for Hill’s men.
Eastleigh take on Essex side Billiricay on Tuesday as Hill’s men will have a well earned rest this weekend.