Ibou Touray opened the scoring in the third minute before Josh March scored on his home debut to equalise for Rovers.
After the break Michael O’Connor put Salford back in front before both Richie Towell and then Ash Hunter were sent off for separate second bookable offences.
Despite an onslaught in the final 10 minutes, The Ammies held out and Graham Alexander couldn’t contain his delight at ending a run of three league defeats.
“[I’m] so happy for the players, the supporters, with what we had to face today and still win was absolutely amazing and so chuffed with everybody because it was a game of football but there was a little bit more and we’ve won the game so absolutely delighted.
“When you’re down to nine men it’s hard to get any attacks going but we had to sit in, dig in and fight for everything and that’s what the players did they were absolutely magnificent, and fully deserved to get that win from character, attitude and commitment.
“That’s what won the game today and that’s, we have to take that forward into other games when we have the quality and the attacking play that we have.
“That’s what we’ve had in the previous three or four games in the league and we haven’t won, we need to get that balance right between how we play, the good stuff that we play and match-winning moments, and we took that today.”
O’Connor was thrust straight into the starting line-up and made a perfect start to his Salford career, but as well as his winning goal his management was stand out for the Gaffer.
“He’s only been in this week and it was a tough decision to bring him in with how well Jack [Baldwin] has played in the previous two games but we’ve brought Michael in for his nous and his influence on the other players around him.
“I thought it took him a little while to grow into the game because he’s only just come and he’s been travelling over from Lincoln but you saw as the game wore on and when you’re getting down to match-winning moments and the difference between the result going one way or the other and fine lines, this is where people like Michael, Pondy, Adam Rooney come into play because they’ve been there, seen it and done it and they can help the players through the game.”
Salford are up to 13th and nine points off the play-offs now, with a Leasing.com Trophy Quarter-Final tie against Accrington Stanley next up on Tuesday.