The Reds’ ninth successive victory in all competitions was secured thanks to an upping of the tempo after a comparatively reserved opening 45 minutes in south Wales.
Wijnaldum’s controlled half-volley from Trent Alexander-Arnold’s corner shortly before the hour put the visitors in front, before Milner’s ice-cool, 80th-minute penalty - earned by Mohamed Salah - allayed any concerns of a late Cardiff comeback.
Jürgen Klopp’s side subsequently move two points above Manchester City again, with Pep Guardiola’s team’s game in hand taking place on Wednesday when they visit Manchester United.
Team news
Three changes were made to the Reds’ starting line-up from the midweek win in Porto, with Jordan Henderson, Naby Keita and Roberto Firmino coming back into the XI.