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Isak, who netted eight league goals in December, struck just before halftime to give Newcastle the lead after falling behind to a Dominic Solanke header in the fourth minute. Solanke's early goal had energized the home crowd in north London, but Newcastle quickly equalized through Anthony Gordon's strike.
Tottenham pressed harder in the second half, with Brennan Johnson hitting the post and James Maddison coming close, but Newcastle held firm through 10 minutes of stoppage time to secure their fifth consecutive Premier League win.
Eddie Howe's team now sits level on 35 points with fourth-placed Chelsea, who play later on Saturday, while Tottenham remains in 11th with 24 points.