The Magpies return to action after the international break with a huge trip to fellow strugglers Norwich, who gave their own survival mission a significant boost last time out with a 1-0 win at West Brom.
Benitez's men will run out at Carrow Road three points adrift of the Canaries and knowing only a third league away win of a desperately difficult campaign will cut out the gap
Barclays Prem
17 Norwich 28
18 S'land 26
19 Newcastle 25
20 A Villa 16
But having worked with Benitez for a little more than two weeks, Janmaat believes the Spaniard is the man to lead the club out of trouble.
The Holland international said: "We have a top-class manager now. We have to believe he can get us to stay in the Premier League.
"He has had a positive effect. It has been organised, the way we played at Leicester and against Sunderland. We have to keep doing that and looking up.
"We feel we can stay in the Premier League, but know we need more wins. We hope and we have the confidence. We must still believe and go out looking to get the job done. I think we can do it."
Newcastle emerged from the clash with Sunderland last time out with a battling 1-1 draw after Benitez's reign had begun with a narrow defeat at Leicester, although a point in the derby was two fewer than the tally for which they had hoped.
However, the manner in which the draw was secured was commendable as they fought back from a poor start to equalise through Aleksandar Mitrovic's late header.
Janmaat, who was by that point back in the dressing room nursing a knee problem, said: "I think it can be a turning point for the team. It was a really well-worked goal.
"I was injured, so I watched from inside, but it was a really good header."