Despite an under-par performance away from home, the visitors were able to claim the victory with goals in each half.
Ryhope took the lead in the 34th minute thanks to a James Ellis penalty.
With 11 minutes of the game remaining, forward Robbie Bird put the game beyond doubt and sealed a 2-0 victory for the away side.
Ryhope were hoping to continue their fine away form, that has only seen them lose three of their 16 away games this season, up against a Redcar side who had won three of their last six.
Gary Pearson made four changes to the side that beat West Auckland in the Durham Challenge Cup semi-final last time out, with club captain Ben Riding returning to the starting eleven having faced a lengthy time out with injury.
Both teams started slowly with the home side having a good chance early on as Michael Woodhouse saw his effort flash across the face of goal.
It was the away side who found the breakthrough on 34 minutes as Ellis was brought down by a Redcar defender in the box and then awarded a penalty.
Ryhope’s top scorer made no mistake with the penalty firing into the top left corner of the goal.
On the stroke of half time Matthew Bateman was forced into a good double save, firstly to deny Ellis and then to deny Oscar Taylor from close range.
Redcar started the second half brightly in pursuit of an equaliser as James Winter was forced into a save to deny Isaac Walker in the 53rd minute.
On the 68th minute defender Jack Proctor got on the end of a freekick in the box but was unable to put his half-volley on target for the home side.
The away side got their second in the 79th minute as substitute Kyle Davis slotted in Bird who cut onto his right and curled the ball into the top right corner of the goal to make it 2-0.
Ryhope kept their clean sheet intact thanks to a Denver Morris block in the 82nd minute to deny Walkers’ effort from just inside the box.
Ryhope will hope to build on their win as they face Bishop Auckland at home in their next game.
After the game, member of the Ryhope management team Craig Hughes said: “We’ve come through it with clean sheet and a win, we would have taken that at the start of the game.”
Hughes spoke of his delight in seeing captain, Ben Riding, return to the team, “It’s pleasing to see, he’s club captain and a leader within the group and he slipped in well today.”
Despite the victory he admitted that it wasn’t Ryhope’s best game. “We lacked a bit of tempo today, it was one of those games when you just need someone to take it by the scruff of the neck but we didn’t really have that, but the three points is the most important thing.”