Varney opened the scoring in the third minute and made sure of the points with a quarter of an hour left after Dave Kitson had restored Pompey's lead following an equaliser from Simon Gillett.
The hosts will next week step up their search for a new manager following Steve Cotterill's switch to Nottingham Forest with Dave Jones, former Doncaster boss Sean O'Driscoll and ex-Manchester United favourite Ole Gunnar Solskjaer among the names being linked with the job.
But caretaker bosses Stuart Gray and Guy Whittingham are holding the fort impressively as the south-coast side made it back-to-back home wins.
They got off to the perfect start when the dithering Rovers defence let Stephen Henderson's long goal-kick bounce and Varney got to the ball before goalkeeper Neil Sullivan to prod it into the net.
It was almost two moments later when Kitson beat Sullivan to another high ball but his goalbound header was weak and George Friend was able to hook it clear.
Kitson planted another header wide before Doncaster finally got into their stride and Henderson had to tip a fierce Kyle Bennett shot around his post.
And Rovers grabbed their 27th-minute equaliser from the resulting corner, John Oster rolling the ball to the edge of the area from where former Southampton midfielder Gillett crashed a sweet, rising drive past Henderson and into the top corner.
Pompey started the second half brightly and defender Ricardo Rocha put a header narrowly wide after Rovers failed to clear Liam Lawrence's corner.
Veteran keeper Sullivan, back in the Doncaster side after an injury to Chris Kirkland, then did well to get down to a low drive from Erik Huseklepp.
Varney sent a snap-shot the wrong side of Sullivan's post and Kitson headed a dangerous Greg Halford cross wide.
At the other end Kyle Bennett 25-yarder flew over the bar before a cross from Brian Stock came off the legs of David Norris and rolled agonisingly wide.
But the second goal Pompey had been threatening came in the 68th minute when Sullivan could not keep out a header from Norris and Kitson followed in to make sure.
And seven minutes later Doncaster were killed off when Kitson played in Huseklepp, who crossed for Varney to sweep his fifth goal of the season past Sullivan.