Coach Watson said: "It was important we won after the week we've had and we believe we are good enough to get back in the top eight even with the points deduction."
Junior Sa'u notched a hat-trick for the second week in a row after a treble in the defeat at Catalans and the win lifts Salford to 10th and above Huddersfield and new basement dwellers Leeds on scoring difference.
Salford swept into a 28-6 interval lead before Rovers hit back in the second half.
But the Red Devils ran in other tries from Robert Lui (2), Niall Evalds, George Griffin and Josh Jones.
The outstanding Gareth O'Brien booted four goals with Michael Dobson landing two against his old club.
Watson hailed O'Brien and said:"Gareth's been brilliant all season and gives us a new dimension. It's his 14th game at full-back and he's going to be a big threat in the position and links up well with Michael Dobson and Robert Lui.
"It was important we got back on the horse to start clawing back the points and it was a really big win."
Salford lost Tommy Lee on his comeback with a knee injury and Josh Griffin also suffered a leg problem with Watson hoping both players will be fit for Saturday's Challenge Cup tie at Castleford.
Rovers replied with touchdowns from Thomas Minns (2), Maurice Blair, Iain Thornley and Ken Sio who suffered a dislocated shoulder scoring his long range try.
SIo earlier booted two goals with Blair adding another conversion.
Rovers coach James Webster, who also lost Graeme Horne with a torn pectoral muscle, said: "Losing Graeme so early on really hurt us but the game was closer than the final scoreline suggests.
"Salford played well and came up with some good plays at the right time.
"We went into the game with a lot of busted people and a depleted squad but did some good things and tried hard.
"Maurice Blair played well as did young Joe Wardill.
"There are 10 games to go and we will come back fighting and have not given up.
"But if anyone has any spare players, please send them our way."
Meanwhile Salford owner Marwan Koukash, set to appeal against the points deduction, announced the club would be holding a press conference on May 16.