The 24-year-old's latest track, Blank Space, rose 12 places to bump her previous number one hit, Shake It Off, from the top after a four-week run.
Swift is the 10th act to score the feat overall, following acts such as the Beatles, Usher and the Black Eyed Peas.
The singer's album, 1989, also scored a third consecutive week at number one on the album chart.
The record has so far sold two million copies and is the second best-selling album of 2014, after Disney's Frozen soundtrack, which has sold 3.25 million copies.