Darlington recorded their first victory since August thanks to a first half goal from striker Barry Conlon.
Rovers began the game brightly and home keeper Andy Collett was called into action in the 3rd minute when easily collecting the 20 yard drive from Bob Quinn.
Darlington replied quickly when Conlon found space inside the area, but his cross was missed by Neil Wainwright and the visitors were able to clear.
The breakthrough was made in the 19th minute when Conlon got to the ball ahead of Rovers keeper Scott Howie to head the ball in from Ryan Valentine's left wing cross.
Ian Clark failed to increase Darlington's advantage in the 25th minute when his poor shot was easily claimed by Howie.
The visitors began to dominate the game and the home side had to thank goalkeeper Collett who pulled off a point blank save to deny Guliano Grazioli, in the 29th minute.
Ray Graydon made a substitution in the 37th minute when the ineffective Simon Bryant was replaced by Lewis Hogg.
Rovers were reduced to 10 men in first-half stoppage time when striker Paul Tait was shown a red card after a head butt on Darlington defender Stuart Whitehead.
The visitors failed to make any impression on the game in the second half. The nearest they came to an equaliser was when Quinn turned and struck a post in the 78th minute.
Darlington manager Tommy Taylor said afterwards, "I am pleased for the players. We didn't play particularly well, but we got the 3 points and they will help our confidence."
Dissappointed Rovers boss Ray Graydon said: "Paul Tait let down himself, me, and his team mates and our fans. His actions stopped us winning the game and he will be dealt severely."