The Millers held their own for much of the opening 45 minutes – and could even have taken a shock lead – but buckled after falling behind to Daryl Murphy’s well-taken strike just before the interval.

Having netted a brace against Birmingham City in midweek, Ritchie repeated the trick with two routine finishes in the second half, Ayoze Perez heading in United’s third in between.

The Magpies’ first sight of goal came with less than two minutes on the clock. Isaac Hayden pulled the ball back for Murphy, whose first-time strike was blocked by Darnell Fisher.

With United’s next attack of note, Jonjo Shelvey picked out Murphy after a neat bit of footwork wide on the left, but the Irishman failed to keep his header on target.

Midway through the half, two openings fell the way of Perez, but the Spaniard failed to make the most of either. First, he made inroads down the visitors’ right, but – with options in the centre – he opted to take aim himself from a tight angle, and debutant ‘keeper Richard O’Donnell turned the ball wide.

Then, after latching onto Murphy’s flick-on, Perez was left with just O’Donnell to beat, only to clear the crossbar from just inside the area.

After a subdued start, Rotherham soon began to grow into the game. Anthony Forde was first to go close, seeing a powerful effort from 20 yards deflect narrowly wide of Karl Darlow’s right-hand post.

Darlow was then forced into a crucial save 38 minutes in. After allowing the ball to squirm beneath his body, the Magpies’ stopper got back across his line in time to deny forward Jerry Yates, who had gathered Forde’s square.

United found their attacking mojo again as the half came to an end, however.

Having just curled over the top himself, Shelvey picked out DeAndre Yedlin’s run with a superb ball, and the American’s low cross was gathered by Murphy, who swivelled before finding the far corner from 12 yards.

And, after the break, Rafa Benitez’s side picked up where they left off.

Yoan Gouffran engineered a shooting opportunity 20 yards out, and O’Donnell was only able to parry the ball straight into the path of Ritchie, who was left with a simple finish.

Aimen Belaid almost pulled one back for the Millers, seeing a dipping strike claimed by Darlow following a corner from the right.

But, just before the hour-mark, Newcastle essentially made sure of victory.

Again, it was Yedlin who provided the assist, racing down the right flank before putting the ball on a plate for Perez, who converted at the near post.

Rotherham substitute Danny Ward then saw a deflected effort squirm wide at the other end, before Ritchie headed off-target from Sammy Ameobi’s cross, the latter returning to action for United after an encouraging loan spell with Bolton Wanderers.

Two minutes later, though, Ritchie did notch another.

The Scot gathered Shelvey’s ball through the centre, and – with time to pick his spot – coolly found the near corner with a low-struck effort.

To their credit, the visitors still carried the occasional threat, and Darlow was forced into a smart parry from Forde late on.

Another three-point haul was long assured for Newcastle by that point, however, the Magpies shifting their focus back to the Emirates FA Cup next week at League One outfit Oxford United.

Newcastle United: Karl Darlow, DeAndre Yedlin (Jamie Sterry 80), Jamaal Lascelles, Ciaran Clark, Paul Dummett, Matt Ritchie, Jonjo Shelvey, Isaac Hayden, Yoan Gouffran (Sammy Ameobi 64), Ayoze Perez, Daryl Murphy (Achraf Lazaar 75).

Rotherham United: Richard O’Donnell, Joe Mattock, Will Vaulks, Richard Wood, Anthony Forde (Stephen Kelly 87), Jon Taylor (Scott Allan 75), Darnell Fisher, Tom Adeyemi, Aimen Belaid, Richard Smallwood, Jerry Yates (Danny Ward 61).

Referee: Jeremy Simpson

Bookings: Newcastle United – none; Rotherham United – Richard Smallwood (45+1).