Tykes striker Davies made it four goals in as many games after latching on to goalkeeper Luke Steele's long kick and steering home the opener in the 30th minute, before volleying home winger Matty Done's cross midway through the second period.
Barnsley were dominant throughout and had it not been for new Rovers goalkeeper Carl Ikeme on his debut, Keith Hill's Tykes would have won by a wider margin, while the visitors played out the last 18 minutes with 10 men after substitute Adam Lockwood had been shown a straight red card for his tackle-from-behind on Stephen Foster.
Doncaster manager Dean Saunders has now lost five of his 10 matches in charge since replacing Sean O'Driscoll in September.
Barnsley boss Hill recalled defender Bobby Hassell, Done and striker Ricardo Vaz Te to his starting line-up, while Doncaster made just one change.
Goalkeeper Ikeme made his first appearance after signing on loan from Wolves last week and was forced into two top-class saves in the first 12 minutes.
Ikeme turned away a 30-yard thunderbolt from Tykes skipper Jacob Butterfield in the fifth minute and then tipped another long-range effort from the same player over the crossbar.
Davies was next to test Ikeme with a shot from outside the penalty area, but the over-worked Rovers goalkeeper could do nothing to keep out Barnsley's route-one opener.
Steele punted forward and Davies pounced on the bouncing ball in the Rovers' penalty area, held off the challenge of defender Shelton Martis and coolly converted, low into the centre of Ikeme's goal from 12 yards to give Barnsley a deserved half-time lead.
Barnsley picked up where they left off at the start of the second half.
Defender Jay McEveley and Butterfield peppered Ikeme's goal with shots from outside the area and, after Doncaster winger James Coppinger had limped off injured - he was replaced by Giles Barnes - Vaz Te spurned a golden chance when dragging his shot wide from 12 yards.
Tykes defender Stephen Foster headed Butterfield's free-kick just wide and Vaz Te flashed an angled 25-yard shot the wrong side of Ikeme's post.
But Barnsley finally doubled their lead in the 64th minute.
Winger Done wriggled clear of two defenders before supplying the perfect cross for Davies to lash the bouncing ball into the top corner.
Rovers midfielder Brian Stock forced Steele into a smart save with his snap-shot soon after, but the visitors' cause looked hopeless in the 72nd minute when Lockwood, a first-half replacement for Martis, was shown a straight red card following his clumsy challenge on Foster.
Butterfield went close with three more shots from outside the area in the last 10 minutes as Barnsley secured their fourth home league win of the season.