Mitchell bagged both for the Swifts while Conor McCloskey and Cathair Friel clawed the Braidman back into it.
Inspired by the marauding Jamie Glackin and the striking powerhouse that is Andrew Mitchell, Dungannon looked irresistible in the opening exchanges.
There were only six minutes on the clock when Mitchell smashed in the opener. An inch-perfect pass from Glackin set the forward clear on the right, he cut back inside and blasted home across the keeper and into the top corner.
The second was a more routine finish on 10 minutes. The striker was well placed to convert after Kris Lowe had bullied Danny Wallace and delivered the cross.
‘Remember the sabbath day...’: Northern Ireland’s biggest Protestant church voices worries over Sunday football as Linfield gets ready to clash with Portadown
Manx Grand Prix: Michael Dunlop gears up for Classic Superbike victory bid on new Team Classic Suzuki GSX-R750
Organisers hope returning Mid-Antrim 150 will become permanent fixture on Irish road racing calendar again
Paul Doolin's focus shift from firefighting to foundations
James Singleton soaking up every minute of Glentoran life
Dungannon looked to have taken the sting out of the game successfully but in doing that, they sat back. Ballymena eventually found some sort of rhythm and after Conor McCloskey saw a 20 yard shot saved, they clawed one back.
It was a well taken header from the winger that beat Andy Coleman as Danny Wallace’s cross unlocked the defence.
And that goal spurred the visitors on into the second half, when it always seemed a matter of time before the equaliser went in.
Ballymena didn’t create that much by way of clear-cut chances but they looked the more likely to finally forge a way through.
And on 60 minutes, it happened. Tony Kane’s free-kick found Cathair Friel, who powered in a header totally unmarked.
Dungannon showed the strength of their bench, bringing on Seanan Clucas and Paul McElroy and they did threaten to bag a winner.
Mitchell’s turn and shot was saved and when Ryan Harpur converted the rebound, he was flagged offside.
Chris Hegarty went close too but his header from Douglas Wilson’s free-kick spun inches wide.
In an end-to-end finish, Andy Coleman went on to save his side.
First he leapt from his goal to intercept a Kane cross with Friel waiting to tap in. Coleman then tipped over a Jenkins header from another troublesome Kane ball into the box.
Neither side could win it and so they’re still tied on eight points.
DUNGANNON: Coleman, O’Rourke, Armstrong, Hegarty, Lowe, Teggart (McElroy 70), Glackin, Wilson, Harpur, Mitchell (Lavery 78), Burke (Clucas 70).
Unused subs: Addis, Hazley.
BALLYMENA UNITED: Blayney, Wallace, Owens, Loughran, Ervin, Millar (Faulkner 66), Jenkins, Kane, McCloskey (Thompson 76), Friel, McMurray.
Unused subs: Glendinning, Gage, Shevlin.