The Dons, who had previously taken only one point from a possible 18, squandered a couple of decent scoring chances before Chris Maguire broke the deadlock after 18 minutes with a clinical finish.
Scott Vernon added a second after 33 minutes when his goal-bound volley took a wicked deflection off Hibs defender Sol Bamba and rolled into the net.
The Aberdeen goalscoring duo combined five minutes after the break to grab a third, this time with Vernon sliding home Maguire's shot-cum-cross at the back post.
Paul Hartley scored a fourth from the penalty spot before Colin Nish pulled a goal back for the visitors after 63 minutes. Bamba headed home a second for Hibs in the final minute of the match but Aberdeen held on to record their second home league win of the season.
Aberdeen brought striker Darren Mackie in for on-loan Rangers attacker Andrius Velicka who dropped to the bench. Defender Andrew Considine was also set to start for the Dons but he was replaced by Jerel Ifil after picking up an injury in the warm up.
Striker Derek Riordan had to be content with a place on the Hibs substitutes' bench with Calderwood giving Ghanaian defender Francis Dickoh a starting berth in his place.
The Dons were looking for the first home win since their opening day of the season success against Hamilton, while Hibernian came to the Granite City in confident mood after beating Kilmarnock last weekend to end their own dire home run that dated back to March.
However it was the home side who should have taken the lead inside three minutes when Vernon showed a neat piece of skill to evade Dickoh's sliding challenge before rolling the ball into the path of Maguire who blasted over.
Maguire was the architect of Aberdeen's next opportunity with a clever back-heel which gave Darren Mackie a chance to test Mark Brown in the Hibs goal but the Dons forward dragged his shot well wide.
Some slack play by Ifil gave the visitors a sniff of goal at the other end after 16 minutes but Mark Howard produced a smart save to deny Nish.
The Dons, however, broke the deadlock two minutes later with a superb piece of counter-attacking play with Sone Aluko's long diagonal pass releasing Maguire who buried the ball clinically into the bottom corner.
The visitors made an enforced change after only 22 minutes when Danny Galbraith came on for the injured David Wotherspoon before Aberdeen's Zander Diamond limped off and was replaced by Derek Young just before the half-hour mark.
The Dons doubled their lead after 33 minutes when Vernon's volley took a wicked deflection off Bamba and trundled past the stranded Brown into the net.
John Rankin should have done better after 38 minutes when he got himself into a promising position but, on his weaker right foot, his low shot lacked the power to beat Howard.
Hibernian made an attack-minded change at the break with Riordan introduced at the expense of Kevin McBride.
But the visitors fell further behind after 50 minutes when Vernon reacted quickest to slide home Maguire's shot on the turn that was heading well wide of the target.
Aberdeen had the chance to score a fourth after 66 minutes when Aluko was brought down in the box by Chris Hogg. Vernon wanted the chance to complete his hat-trick from the spot but in the end it was Dons skipper Paul Hartley who sent Brown the wrong way from 12 yards.
Nish pulled a goal back for the visitors two minutes later when he headed home Paul Hanlon's cross, although the striker landed awkwardly and had to be replaced by Valdas Trakys immediately afterwards.
The visitors were appealing for a penalty with just under 15 minutes remaining when Dons' makeshift defender Young collided with Galbraith but referee Craig Thomson waved play on.
Bamba headed home a second for Hibs from Riordan's accurate cross in the closing stages but despite this late rally from the visitors the majority of the 7,587 at Pittodrie left content having seen their team win at home in the league for the first time since their 4-0 victory over Hamilton.