Jordan Houghton equalised in the 45th minute Callum Kennedy's brilliant free-kick and the previous week's 90th-minute match-winner, Liam Mandeville, converted two penalties to seal the points.
Goalkeeper Marko Marosi had recovered from the blurred vision which forced him off midway through the first half of the 2-1 win against Hartlepool to take his place in the Rovers side. It was fortunate in that his replacement, Ross Etheridge, fractured a finger in the same game and would have been unable to face Orient - young Louis Jones being on the bench to cover for Marosi.
Manager Darren Ferguson was, therefore, able to name an unchanged starting line-up against an Orient side led by Andy Edwards following the midweek sacking of Italian Alberto Cavasin with them hovering just above the drop zone. Edwards, who has had two previous caretaker spells in charge, has been appointed until the end of the season.
Rovers were unfortunate not to be ahead by the 17th minute. James Coppinger's free-kick was headed back across goal by Andy Butler and Alex Cisak threw up an arm to divert John Marquis's close-range header over the bar.
From the flag kick, Tommy Rowe's deft flick was diverted against the bar by Cisak's reflex save and Butler's follow-up header struck the woodwork before being cleared for Rovers' fifth corner.
However, it was Orient who took the lead in the 19th minute when Jay Simpson won a free-kick 35 yards out in the centre of the field. Left-back Kennedy produced a peach of a delivery, curling the ball inside the post as Marosi dived full length to his left.
Rovers were out of luck when Mandeville took a return pass from Rowe and, from just inside the left corner of the area, curled a shot against the bar in the 31st minute.
James Coppinger also saw a goalbound drive deflected over the bar by central defender Tom Parkes as the pressure built.
It finally brought the equaliser in the 45th minute when Orient failed to clear Rovers' seventh corner and Houghton drilled the ball home from the edge of the area.
Matty Blair immediately saw a shot pushed aside for a corner after the break and Coppinger hit wide of the far post when the ball was worked back to him.
Appeals for a penalty for hands by Myles Judd went unheeded before Rovers took a 59th-minute lead.
Matty Blair burst into the area and was tripped by substitute Josh Koroma leaving Mandeville to send Cisak the wrong way from the penalty spot.
He went to the opposite side seven minutes later to make it 3-1 after Parkes had brought down Rowe following an arcing run from the right into the area.
Orient went close but a fierce header from substitute Paul McCallum was pushed away by Marosi down to his right for their first corner in the 76th minute.
That was close as the visitors came and Rovers finished well on top as the freezing fog descended.