The Swans made it nine games unbeaten in all competitions as goals from Conor Hourihane, Matt Grimes and Jay Fulton gave them victory at the New York Stadium.

Freddie Ladapo had halved the deficit for Rotherham but defeat leaves them still in the drop zone.

The only chance of a scrappy opening 20 minutes was carved out by Rotherham full-back Wes Harding who cut in onto his stronger right foot and saw his effort deflected just wide for a corner.

Swansea showed their first sign of class as they took the lead after 28 minutes through Aston Villa loanee Hourihane.

The move started with Andre Ayew picking out Connor Roberts. His cross was only half cleared and the Republic of Ireland international lashed the ball into the bottom corner from the edge of the box.

Jamal Lowe had a good chance to double the lead but his strike from the edge of the box was pushed wide by Jamal Blackman.

But from the resulting corner, after 38 minutes, they did go two up with Grimes firing in from just outside the box.

The in-form Matt Crooks tried to get Rotherham back into the contest before the break but the shot at the end of his mazy run was just over the bar.

The Millers made attacking changes at the interval with Ladapo brought on to partner Michael Smith up top and Ryan Giles adding more threat down the left.

Ladapo snatched at his first half-chance after Richard Wood had burst forward from defence.

Rotherham's defence had to scamper to crowd out a dangerous counter-attack led by Lowe but the ball eventually fell to Roberts whose effort was easily gathered by Blackman.

The Millers went direct to get a goal back after 65 minutes, with Harding's long throw causing Swansea's defence issues and Ladapo was on hand to head past Freddie Woodman from close range.

The home side were energised by the goal and continued to threaten as Giles found Crooks with a left-wing cross, but his header was easily gathered by Woodman.

Swansea needed a third to regain their control on the game and it came in the 74th minute with Fulton netting with his first touch after coming on.

Fulton was on hand to finish clinically with the outside of his right boot after being found by a left-wing centre from Jake Bidwell.

Rotherham continued to make life uneasy for the Welsh side with Clark Robertson heading against the woodwork.

Swansea had a chance to make the scoreline more secure but Blackman forced Lowe's header over the top of the bar.