The teams were greeted by driving rain as Rovers started the brightest. Russell's chest pass saw Rigoglioso draw a diving save from Danny Alcock inside 30 seconds.
Then Mark Preece's incisive pass opened up a chance for Michael Brough, but the former Rangers midfielder saw his skidding strike smartly turned around the post by Alcock.
Nonetheless Rangers responded. Kevin Street arrowed in a ninth minute cross that Ged Murphy nodded just over Steve Williams's bar.
Meanwhile drama ensued on 12 minutes. Craig McAughtrie appeared to upend Alex Meechan but Rovers' protests were waved away.
At the other end Darren Jones did well to nod the ball away from 41-year-old Neil Grayson with Williams rooted to his line before Street rattled the underside of his crossbar in the 14th minute as Phil Robinson's side looked to get a foot hold in the game.
However, three minutes later Rovers were ahead. Brough was adjudged to have been brought down by Robin Gibson. Simon Clist's resultant free kick picked out the unmarked Russell who headed home at the far post for this third goal of the season.
Rovers went close again on 32 minutes. Again, from an identical position Clist swung over a free kick that saw Brough a fraction away from getting his head to the ball.
Rangers almost grabbed parity on 36 minutes. Murphy arrowed in a cross that saw Grayson's bullet header superbly tipped away by Williams.
On the cust of the interval, Rovers' Rigoglioso saw his fizzing strike from the edge of the box hit the post as Harvey's side finished the half in the ascendancy.
Rangers opened the second period with the ineffectual Guy Madjo replaced at half time by Danny Edwards.
Meanwhile Grayson saw his strike hit the face of Jones as Rangers started the second period in a positive fashion, while Jones nearly made it two at the other end as he nodded over from Clist's inviting cross.
Rangers did equalise on 52 minutes. Substitute Edwards saw his raking cross from the left pick out Gibson whose strike deflected off Jones on its way past Williams.
However parity only last two minutes as Rovers regained the lead. Meechan's header found Rigoglioso who thundered home a 54th minute right-footed volley from outside the box to give Alcock no chance.
Rigoglioso almost engineered the third for Rovers. His cross from the byline saw a grounded Alcock acrobatically claw away Clist's 63rd minute strike.
With 12 minutes remaining new boy Matt Robinson came off the bench for Rigoglioso as Jim Harvey reverted to just substitute Mark Beesley as a lone striker. And it was Beesley who came close to scoring a third on 86 minutes, but he couldn't apply the final touch after fine approach play from substitute Les Afful.
With four minutes of stoppage time added on it was nerve jangling moments for Rovers who, despite sustained Rangers pressure, held on to record their first victory of the season.