Hull City 4 Rotherham United 1: Tigers turn on the style, Millers' dismal away form just turns on more alarms

Liam Rosenior has built an impressive squad in East Yorkshire and they were enjoying showcasing their skills on a cold night but in the back of your mind you had to remember – this was Rotherham United away.

The Millers at home are a prospect to be feared. Dogged and determined, they had taken points off Ipswich Town and Leeds United but their last two away performances had been bad enough to get Matt Taylor the sack as manager.

This one might have ended caretaker Wayne Carlisle's chances of getting the job permanently.

Because as soon as Tyler Morton gave his side a fifth-minute lead, Rotherham just crumbled.

Winning 4-1 was a lot of fun for them and there were some lovely skills on show from a talented whose confidence will have been boosted by it, but it was sweets-from-a-baby stuff. All the fight Rotherham show seems to be under lock and key at the New York Stadium.

Jaden Philogene's backheeled goal four minutes later, Liam Delap's lovely turn from a fizzed Morton pass, the midfielder's backheeled to set in train the 20th minute third goal, Jacob Greaves' Franz Beckenbauer, all of them screamed a home team having a whale of a time.

If you were one of the Hull fans chanting "Acun give us a wave" – of course owner Ilicali obliged but Tom Eaves could not when he came on as a substitute against his old club – or telling goalkeeper Ryan Allsop to shoot with the ball at his feet just inside his own half, this was a day to enjoy football for all it is. Who cares about the opposition, make the most of it.

But if you were one of the miserable Millers sarcastically chanting "We've got the ball" there cannot be many more miserable ways to spend a freezing Tuesday night.

What made it worse for them was that it was Rotherham who got the ball rolling.

On his first appearance since early October, it was Grant Hall's poor backpass that sent Delap through one on one. Viktor Johansson came out to deny him but could only set up Morton.

Suddenly Carlisle's positive 4-4-2 did not look so clever, the hatches flapping in the wind when in hindsight they could have done with being battened down by a club now with one point from nine away Championship matches.

When Jason Lokilo's cross bounced off Dexter Lembikisa, Philogene had the audacity to backheel his second goal four days and set the mood for what was to follow.

Rotherham had four first-half shots but no good ones. Hull's confidence was in danger of spilling over.

What faint hopes there might have been of a comeback died in the 20th minute, Morton backheeling a back-to-front ball to Delap, Johansson taking the sting out of his shot but only presenting Scott Twine with a shot at an open goal from a yard to open his goalscoring account for Hull.

Five minutes before half-time Twine turned provider as Greaves galloped up from centre-back, turned his man and forced another save.

The interval brought no let-up, Twine having a shot blocked within a minute of the restart. By the 48th minute, it was four.

Hall touched Lokilo's cross into the path of Twine, who saw his shot was blocked by Lemibikisa. But Philogene was next in the queue, hitting home the rebound.

Rosenior will have been more angry than Carlisle was happy when Hall converted a relatively free header at a 59th-minute corner.

Hull's substitutes only added fresh quality although the intensity inevitably dipped. Adding four minutes was just cruel on players and fans who probably wanted to get into the warm by then.

The Tigers moved back into the play-off places, their confidence plumped up, but Rotherham's problems on the road look set in. Two goals to give Queens Park Rangers a 4-2 win over Stoke City made their miserable night worse, dropping them a place in the relegation zone.

Never mind a new manager, they urgently need a psychologist.

Hull City: Allsop; Christie (McLoughlin 72), Jones, Greaves, Coyle; Seri (Traore 63), Morton (Slater 83); Philogene (Tufan 63), Twine, Lokilo; Delap (Connolly 73).

Unused substitutes: Ingram, Docherty, Vaughan, Smith.

Rotherham United: Johansson; Lembikisa, Morrison, Hall (Peltier 67), Bramall (Appiah 58); Rathbone, Odoffin (Lindsay 67), Tiehi, Revan; Hugill (Eaves 67), Kelly (Nombe 77).

Unused substitutes: Phillips, Ayala, McGuckin.

Referee: R Welch (Washington).