The home side had taken an early lead through Scott Vernon, but Gavin Gunning turned home a leveller, and Dons goalkeeper Jamie Langfield put through his own net to give the Arabs an unexpected half-time lead.
However, top scorer McGinn blasted a free-kick into the top corner to level the scores, and see that both sides began 2013 with a point.
Before kick-off, the selection which caused the biggest stir was the inclusion of John Souttar at right-back for Dundee United. The Aberdeen-born 16-year old was making his debut in his home town, and entered the record books as the youngest man ever to play for the Arabs at 16 years and 99 days.
The home side had the lead after 11 minutes. Joe Shaughnessy slipped a neat ball inside full-back Barry Douglas, and recalled winger Ryan Fraser hit the bye-line before pulling the ball back for Vernon to stroke home from six yards.
They could have had another shortly after, when Souttar's slack pass allowed McGinn to run from his own half. He checked, awaiting support, before opting to go himself, only to see his eight-yard shot palmed onto the woodwork by United keeper Radoslaw Cierzniak.
But the visitors were on level terms after 20 minutes. Daly's effort from a Douglas free-kick was saved by Langfield but he couldn't hold onto it, and Gunning threw himself at the ball to find the net from close range.
And they could have gone in front five minutes later had Johnny Russell not been so wasteful after an incisive counter-attack.
Jonny Hayes' corner was headed clear at the near post, allowing Stuart Armstrong the freedom of Pittodrie on the left. He played in Russell at the edge of the Dons area, but the striker shot straight at Langfield.
The striker passed up an even better opportunity just before the half-hour when Willo Flood dinked a neat pass into his path, but with only Langfield to beat he blazed over the crossbar.
He was again involved when his side did take the lead after 34 minutes- but it was Langfield who had the travelling support singing his name.
Russell sent in a low cross from the left, which Langfield seemed to have covered but, perhaps distracted by the run of Flood in front of him, the goalkeeper allowed the ball to slip through his legs and into the net.
The home side were back on level terms after 53 minutes, and it was top-scorer McGinn who grabbed the equaliser. Referee Alan Muir deemed Gunning to have fouled the former Celtic man as he went up for a header, and McGinn crashed his 20-yard free kick high past Cierzniak and into the top corner.
It was a nervy ending for United as Cammy Smith saw a low shot saved by Cierzniak, before a superb recovery challenge from Gunning denied McGinn, after Gunning's own hesitation seemed to allow the striker through on goal.