Referee Keith Hill awarded the spot-kick after United's George Friend brought down Keigan Parker and Abbott slotted into the right corner, sending goalkeeper Steve Mildenhall diving the wrong way.
Goalscoring chances had been at a premium although referee Hill had ruled out efforts by Parker for offside and Friend for a foul in the opening 45 minutes.
A back-tracking Mildenhall turned over Abbott's chip and Latics keeper Dean Brill parried a close-range Roy O'Donovan shot in the opening period.
After the break Mildenhall saved Danny Whittaker's scuffed effort, Alan Sheehan was inches over the bar with a 20-yard strike and Shrimpers skipper Adam Barrett diverted Parker's shot over his own crossbar.
Southend pushed forward looking for an equaliser and blew a great chance when Francis Laurent fired wide from close range.