A James Thomas penalty and a disallowed Southend goal were enough for success starved Swansea to record a fortunate first win under Brian Flynn.
Thomas coolly slotted home his fifth league goal of the campaign in the 52nd minute after referee Mick Fletcher adjudged Lee Jenkins had been felled by Mark Beard in the box.
Referee Fletcher had already been in the thick of the action and travelling Shrimpers fans were outraged when the Worcester official ruled out a Phil Whelan effort that found the back of the net after 15 minutes.
Freestone made a complete hash of Kevin Maher's cross and looked on his horror as his punch directed the ball towards his goal, but Fletcher spared Freestone's blushes when he indicated that makeshift striker Whelan was the one who had handled and promptly booked him as a result.
Swansea were unlucky not to have taken the lead after 34 minutes when Jason Smith smashed a Paul Reid corner on to the crossbar. The centre half seemed to have controlled the cross with his hand, but was still free to test the strength of the Vetchfield woodwork.
The in-demand man in the middle looked like he wanted to make amends to Southend boss Rob Newman as he played seven minutes added time.
But a determined Swansea side held out in a final period of frenzied football that was more akin to a cup final than a mid October league encounter.
But Flynn promised more of the same: "We just have to grind out as many wins as possible.
"And when we are safe we can worry about the type of football we are playing."
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