Chelsea loanee Kenedy scored the Magpies' opening goal after just two minutes at St James' Park before adding another on the half-hour mark.
Ritchie then scored Newcastle's third on 57 minutes, his second in his last three matches after netting the winner in the Tynesiders' 1-0 victory over Manchester United.
Ritchie, however, has urged the fans not to get carried away in terms of their improved performances and standings, insisting that there is still work to do before survival can be deemed certain.
"We need to take one step at a time," the 28-year-old told NUFC TV. "We've had a few good results, we need to continue to work hard, do what we have been doing.
"Details of things that we have maybe not been so good at earlier in the season, we've now put right and performances are coming together as a whole now and we're performing really well as a team.
"We need to continue to work as we have been, concentrate on that and hopefully we can keep picking up points.
"Every three points now is massive, it's huge. We need to get to that 40-point mark ASAP and three points is a good step in the right direction."
Newcastle are next in Premier League action at home to Huddersfield Town on March 31.