McCluskey and Topley came on for Dungannon at half-time and the duo's introduction gave impetus to the Swifts.
Swifts levelled just seven minutes later when McCafferty scored his seventh league goal of the season.
The Swifts had led through Michael Ward's 12th-minute goal but Ards equalised through a Jason Hill penalty.
They had an early scare against the Swifts as Timmy Adamson forced a save from keeper Elliott Morris.
Two IFA Premiership football games - Glentoran v Dungannon Swifts and Donegal Celtic v Linfield - were postponed.
Dungannon Swifts edged out Donegal Celtic 4-3 in a Suffolk Road basement clash.
The 21-year-old Boyce arrives at the club two weeks after midfielder Shane McCabe moved to the Glens from Dungannon Swifts.
BBC: Darren Boyce could make his Glens debut in the Irish Cup
Lastly, keep an eye out for swifts, whose numbers, as in other parts of the UK, are on the decline.
Swifts responded seven minutes later through Neil MCafferty's 30-yard drive, which crept into the bottom left of Davy O'Hare's goal.
"It was a great chance to get back into football after eight months out, " said the former Dungannon Swifts boss.
Adamson should have put Swifts ahead after 74 minutes but Matt Crossan, who was injured as a result, blocked his effort.
Swifts defender Adam McMinn scored an own goal in trying to clear a Burrows shot and sub Johnny Black made it 3-0.
Dungannon Swifts survived a scare at Dergview, coming from a goal down to level at 1-1 and then winning 4-1 on penalties.
The Glens join Portadown, Coleraine and Dungannon Swifts in the last four.
BBC: Glentoran beat Linfield on away goals in quarter-finals
Trinidad wing Johnson has impressed in two pre-season games and Smith hopes to take him to Northern Ireland to face Dungannon Swifts and Cliftonville.
BBC: SPORT | Football | My Club | Wrexham | Wrexham struggle for Johnson cash
Captain Jody Tolan and Darren Boyce both had chances to give the Bannsiders the lead but failed to beat Rouse in the Swifts goal.
Dermot McCaffrey started the Swifts comeback before a Timmy Adamson double clinched victory for the County Tyrone side and a move up to eighth place.
Substitute Tommy McCallion's superb through-ball split the Swifts defence and Patterson slotted past Rouse at his near post for his seventh league goal of the season.
Fitzpatrick then equalised for the Swifts, Scullion's left-foot shot made it 3-2 on 85 minutes and there was still time for Ward to fire in a fourth.
However, Glenavon restored their lead within two minutes as Grant powered a close-range header past O'Neill after the Swifts keeper had only been able to parry a Molloy pile-driver.
Lisburn Distillery pair Glenn Ferguson and Pat McShane return to their former club Linfield with the champions aiming to bounce back from last Saturday's 2-1 defeat at Dungannon Swifts.
The Carling Northern Ireland Football Writers Goal of the Month was awarded to Niall Henderson in recognition of his goal for Dungannon Swifts in their 2-1 defeat by Ballymena United on December 11.
As the match entered injury-time, a 1-1 scoreline loomed but McAllister then looked to have secured the points for the Swifts when he bundled home from close range after good work by Darragh Peden.
McCaffrey blasted in number two with a fine left-foot strike in the 81st minute to make sure of a win which takes Dixie Robinson's Swifts above Coleraine and into fourth place in the Carling Premiership table.
The Lurgan Blues have won six, drawn five and lost 16 of their 27 league games this season and are now two points adrift of Newry City and Dungannon Swifts at the bottom of the table.
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