The former One Direction singer notched up combined sales of 112,000, including 4.97 million streams.
In the album charts, David Bowie became the first artist since Michael Jackson to knock himself off the top spot.
The 2002 release Best of Bowie replaced Blackstar, Bowie's last album, released days before his death in January.
Malik's Pillowtalk replaced Shawn Mendes' Stitches at the top of the singles chart, with Mendes falling to number three behind Fast Car, from Jonas Blue ft Dakota - a dance version of Tracy Chapman's 1988 single