After a goalless first 45 minutes, a much-changed Reds side fell behind early in the second period.
The visitors upped the ante following Jack Cork’s opener, though, and responded rapidly through goals by James Milner and substitute Roberto Firmino.
Shaqiri, one of only four players to retain their starting berth from Sunday’s Merseyside derby, then applied the finishing touch in stoppage time when he rounded off a lightning-quick counter-attack with aplomb.
Victory keeps Liverpool, who remain unbeaten in the Premier League this season after 15 matches, within two points of table-topping Manchester City.
And the No.