Linfield went into the game needing a point to guarantee the club's 49th Irish League title.
"Ballymena were well organised and hard to break down, " said Linfield manager David Jeffrey.
Linfield captain Noel Bailie rescued his side with a superb goal-line clearance five minutes from time.
The goal keeps Linfield two points behind Glentoran and the Blues have a game in hand.
Reports last week suggested Linfield had rebuffed the offer for the Northern Ireland international.
James Costello set up Miskimmin's early chance as the former Linfield striker lashed against the woodwork.
The agreement between the IFA and Linfield, signed in 1984, stretches for another 80 years.
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Linfield are now consulting with their lawyers over the governing body's attempt to end the contract.
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Jamie Mulgrew ran unchallenged to hit Linfield's third on 50 before Keith Gillespie's reply on 63.
Another Glentoran goal would have had strained Linfield nerves and the chances did come late on.
Linfield manager David Jeffrey admitted the holders were lucky to get away with the 0-0 draw.
"At this moment in time Conor is very much a Linfield player, " added Jeffrey.
Earlier in the day the Linfield player had celebrated the birth of a son.
Norwich City had also made an offer but Linfield said it had been unacceptable.
Scott Young's team is five points behind pacesetters Linfield, who beat Portadown 2-1 on Friday night.
More unselfish work by McAllister enabled Peter Thompson to fire Linfield's third goal on 45 minutes.
Linfield's lead was not threatened until injury-time when Chris Scannell fired a great chance over the top.
Linfield appeared content that the job was done but Thompson added a fourth three minutes from time.
Fothergill and Linfield couldn't use lights or normal cameras because they would have frightened away the animals.
"He's very much a team man and that certainly fits the ethos here at Linfield, " he said.
Linfield manager David Jeffrey had said on Tuesday that he was resigned to losing his top scorer.
Thompson netted 44 times last season to help Linfield claim a third successive league and cup double.
In the 88th minute, Philip Lowry found Allen who scored with a 15-yard left-foot shot for Linfield.
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Linfield's out-of-contract keeper Alan Mannus got a late run and made a great save to deny Pellissier.
Linfield came close to equalising on 55 minutes as Robbie Garrett's fierce free-kick hit the Newry woodwork.
It was a hard-earned win for Linfield against a Ballymena team desperate to end a run of defeats.
Murphy's penalty ended any remote chances of a Coleraine revival as Cliftonville stayed two points behind leaders Linfield.
Northern Irish champions Linfield could play Steaua Bucharest if they beat Gorica of Slovenia in the first qualifier.
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Crusaders' win moves them level on points with second-place Glentoran with both teams five points behind leaders Linfield.
Two IFA Premiership football games - Glentoran v Dungannon Swifts and Donegal Celtic v Linfield - were postponed.
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