The ex-Inter man passed former record-holder Juninho as he levelled the game at the Britannia Stadium, scoring his 30th goal in the top-flight.
Juninho had previously seen his mark equalled in Coutinho's last Premier League run-out, when he hit the net against Bournemouth.
30 - Philippe Coutinho has scored more @premierleague goals than any other Brazilian in the competition's history. Record.— OptaJoe (@OptaJoe) 8 de abril de 2017
Coutinho, however, may soon face competition from a team-mate for the record.
Compatriot Roberto Firmino added the second of the game for Liverpool to put the Reds 2-1 ahead, his 20th strike since moving to Anfield from Hoffenheim in 2015.