The visitors also hit the bar twice against a Motherwell side who looked flat following their Europa League exit in Russia in midweek.
Aberdeen's win over last season's runners-up builds on their opening Scottish Premiership victory over Kilmarnock and is a sign of real promise that they can mount a challenge in the top half of the table after four years in the bottom six.
The Dons were ultimately convincing winners against a side they had not beaten in 15 league games since a 2-0 win under Jimmy Calderwood in November 2008.
Both Mark McGhee and Craig Brown failed to take three points against their former club, although the latter enjoyed two cup wins, but it was first-time success for Derek McInnes, who stretched his unbeaten run as Dons boss to seven games.
The game did not start with such promise for Aberdeen and their official travelling support of 1,879, who were silenced with 40 seconds gone.
Keith Lasley headed the ball forward for John Sutton midway inside the Dons half and he turned and played the ball through the middle of the Dons central defence for Anier to run round the outside.
Just as he had done when scoring a late winner at Easter Road last weekend, the Estonian showed real composure as he waited for Jamie Langfield to go down stroking the ball over him and inside the near post.
Aberdeen, who were without the injured Barry Robson, had two chances to level inside 10 minutes. McGinn had the first when he was played down the right channel by Willo Flood but Lee Hollis got down to block the shot.
Pawlett broke quickly after a Motherwell set-piece failed to come off and McGinn found Ryan Jack 20 yards out but he curled his effort beyond the far top corner.
Motherwell, who had James McFadden Sutton and Iain Vigurs back in after they were left out of the trip to Kuban Krasnodar, had a good spell of possession during which Dons defender Joe Shaungnessy almost put through his own net with a clearance.
But the visitors hit the bar again in the 29th minute when Calvin Zola sidestepped McManus on the right edge of the penalty area and curled the ball over Hollis.
Zola had an ideal chance to level two minutes after the restart when Flood set him up in space 14 yards out following another counter-attack but the summer signing from Burton completely missed his kick.
There was more misery for the Dons moments later when Russell Anderson went off with what looked to be a hip knock. Clark Robertson came on at left-back and Reynolds moved inside.
Zola had another chance when a Jonny Hayes cross fell for him beyond the back post but he fell back as he shot wide.
But their equaliser soon came in the 62nd minute following some poor play in the Motherwell defence. Stevie Hammell was in yards of space as he tried to bring down Robertson's high diagonal ball just inside his box but he miscontrolled and Hayes burst on to it and ran at McManus.
The Scotland defender dived in and brought the Irishman down before McGinn sent Hollis the wrong way from the spot.
Aberdeen continued to look the more likely team and took the lead after McManus had been penalised for a push on Josh Magennis. Reynolds broke free from his marker to powerfully head home Hayes' free-kick.
Hollis saved with his legs from Magennis after McGinn's cutback and John Beaton pointed to the spot from the resulting corner, although the infrongement was not obvious. McGinn found the same corner with his 84th-minute effort.