Low struck the opener just moments after the interval and McGinn curled a fine effort into the far corner of the net after 66 minutes to secure the points.
It took a while for the match to catch light but suddenly, after 15 minutes, it was as though a switch had been flicked, and the chances started coming thick and fast. Three times in as many minutes, the home side could have been in front.
Peter Pawlett's teasing cross was cleared by Kallum Higginbotham for the first in a series of corners during which Paul Gallacher got down to turn away a Goodwillie header, and Mark Reynolds saw Thistle's new left-back Jake Carroll clear off the line.
The Jags looked bright on the counter-attack but they were struggling to put Jamie Langfield under any serious pressure. The goalkeeper did, though, fluff his lines with a clearance which barely left the penalty area, but the visitors could not capitalise.
Gallacher was certainly the busier of the two goalkeepers and he was called into action again to deal with McGinn's low drive before Aberdeen really started to turn the screw.
Johnny Hayes, anonymous in the opening half-hour, suddenly sprang into life. His weaving run ended with a teasing cross that fell to McGinn six yards out, but the former Celtic man could not adjust his feet and Gallacher mopped up.
Just a minute later, Hayes again set off on a dash down the left but a he tried to hold off the attentions of Stephen O'Donnell, he failed to get a cross in. For his efforts, O'Donnell picked up the game's first booking.
Aberdeen were threatening down both flanks and Thistle could breathe a sigh of relief once more when Abdul Osman turned Shay Logan's tempting right-wing delivery behind for another corner.
The chances began to fizzle out as the half drew to a close, with Higginbotham's booking for dissent the last real incident of the first half.
But it took no time at all after the restart for the home side to open the scoring. Low was fed the ball 20 yards out and he curled an unstoppable shot, left-footed, past Gallacher from 20 yards.
Partick's response was to introduce Kris Doolan in place of Christie Elliot and within seconds the visitors had their best chance so far. The ever-dangerous Higginbotham struck towards goal, but Langfield was equal to his effort.
It was an important save at an important time, and five minutes later Aberdeen edged closer to three points. Even on his quieter days, McGinn is capable of coming up with something special and he did just that as the rain came teeming down at Pittodrie.
From outside the penalty area, he swung a superb arcing shot across the goalkeeper and into the far corner of the net, his first goal of the Dons league campaign.
As the game entered the final 15 minutes, injuries to Hayes and Thistle defender Conrad Balatoni forced the duo off the park, replaced by Barry Robson and Aaron Muirhead respectively. Aberdeen then replaced the impressive Low with Cammy Smith, and Partick's Steven Lawless took the place of Ryan Stevenson.
Five minutes from time, Gallacher made yet another fine stop, pushing Robson's driven free-kick onto the crossbar and the goalkeeper's excellent performance should not be tarnished by the result.
Aberdeen brought on Adam Rooney for Pawlett in the dying minutes, but the striker had little time to make an impact on proceedings.