Haris Vuckic and Yoan Gouffran got the Magpies off to a fine start with early goals and although Iain Vigurs hit back for the hosts, Moussa Sissoko restored their two-goal advantage heading into the interval.
James McFadden converted a clever penalty after the restart to cut Motherwell's deficit, but Newcastle again showed their class with a fourth from substitute Sylvain Marveaux as they wrapped up a comfortable win.
Motherwell started without new signing Stephen McManus and they fell behind after just eight minutes. Well keeper Lee Hollis made a brave block at the feet of Gouffran, only for Vuckic to slot home the rebound.
Vuckic then returned the favour on the quarter-hour when the Slovenian playing in Goufrann, who fired a shot underneath Hollis to double their lead.
Motherwell pulled a goal back on 26 minutes when Vigurs drilled a low effort past Rob Elliot from 18 yards, but Newcastle finished the half strongly and struck again when Sissoko's meek shot squirmed under Hollis' body.
Sissoko undid his good work early in the second half when he tugged down Stuart Carswell in the area, and McFadden chipped his penalty straight down the middle.
That act of ingenuity mattered little, however, as Marveaux netted a fourth for the Premier League side on 65 minutes from Paul Dummett's low cross to the back post.