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 close the gap.
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 Netherlands 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."
His comments come days after Netherlands manager Danny Blind suggested Janmaat would leave St James' Park in the summer if they get relegated to the Championship.
"Janmaat regretted terribly that he had to cancel [joining up with the squad with a knee injury]," Blind told Dutch newspaper De Telegraaf.
"He wanted to be with the Oranje [as he was] keen to be in the spotlight for another club in case Newcastle United are actually relegated."