The Reds led 10-6 until Taylor blasted through poor defence twice in six minutes to seal the win, making up for a disappointing derby show against Hull on Good Friday.
Sandercock said: “It was a badly needed victory and every win is like gold because we are not in the top eight.
“We defended well and were rewarded for our hard work.
“Both sides were guilty of pushing passes and it was a pretty scrappy game.”
Salford, who have now been overtaken by Rovers in the table, led with tries from Luke Patten and Ashley Gibson, with Lincoln Withers replying.
But Taylor then struck at the double and Sandercock said: “Scott had an outstanding second half but in the first half was a little down on what I expected.
“Then he made his presence felt and came up with two big plays which won us the game.”
Rovers lost Joel Clinton with an ankle injury and Sandercock said: “Joel will have a scan tomorrow but hopefully it is not too serious.”
Salford forward Vinnie Anderson was taken to hospital with a suspected fractured elbow.
Salford boss Phil Veivers blamed his side’s defeat on errors.
He said: “The conditions had a lot to do with the mistakes but we are filthy with ourselves because we led 10-6 until 12 minutes from time. The game was there for us to win and we should have won but conceded two soft tries.”
Salford: Patten, Gibson, Moon, Gleeson, Williams, Holdsworth, Smith, McPherson, Godwin, Paleaaesina, Ashurst, Neal, Wild. Substitutes: Howarth, Anderson, James, Jewitt.
Hull KR: McDonnell, Hall, Welham, Horne, Latus, Murrell, Dobson, Paea, Withers, Taylor, Mika, Cox, Galea. Substitutes: Clinton, Watts, Carlile, Peterson.
Referee: T Roby (RFL).