Newcastle showed promise in defeat, even though it was like watching paint dry.
Newcastle, while defensive, looked confident in their tactics following Wednesday's shock win over Manchester City.
Their wing-backs - DeAndre Yedlin and Matt Ritchie - tucked in to make a narrow back five and Spurs were repeatedly forced left.
Jan Vertonghen had delivered nine crosses by half-time, his highest mark in the Premier League, as Newcastle's plans largely worked.
And with Rondon a presence up top they had chances of their own. He saw an effort blocked in the box before the break and perhaps should have opened the scoring after the interval when his guided header hit the post with Hugo Lloris beaten.
Ayoze Perez also warmed the hands of the Spurs keeper from long range in the second period as Newcastle showed pockets of threat for their 28% possession.
They could have been better on the ball for periods, but Benitez will look at the dogged displays of Schar and Jamaal Lascelles as positives, along with the general resistance his side offered.
January addition Antonio Barreca came off the bench for his debut late on, while record signing Miguel Almiron was ineligible while he awaits a visa.
If the new £20m forward brings the quality fans crave, gutsy displays like this will at least give him a solid platform from which to perform as they look to climb the table after a result which leaves them 15th.