Daryl Murphy grabbed the first hat-trick of his League career as Town took a step closer to the top six with a comprehensive win at the New York Stadium.
The Republic of Ireland international struck either side of half-time to put Town four goals to the good after Brett Pitman had given Blues an eighth minute lead and Jonathan Douglas had got on the scoresheet for the first time since his summer arrival.
Rotherham had their fans dreaming of a sensational comeback after fantastic goals from Brandon Barker and Matt Derbyshire reduced the arrears before the hour but Murphy became the first Blue to score a hat-trick since Connor Wickham in 2011 when he beat Lee Camp with an excellent finish 18 minutes from time.
Mick McCarthy made one change to the side that beat Bolton in midweek, Douglas coming in for Ainsley Maitland-Niles, who dropped to the bench. Rotherham included three former Town loanees in their line-up, Danny Collins, Frazer Richardson and Paul Green.
Blues could have been in front inside the first minute, Dean Gerken’s clearance downfield wasn’t dealt with and Freddie Sears pounced to fire at goal from inside the Millers’ box but Camp was equal to the task.
Town carried a real attacking threat from the first whistle, Sears forcing a corner then Tommy Smith firing over after Christophe Berra had fed the ball back into the box.
The warning signs were there for Rotherham and it was no surprise when Town took the lead on eight minutes, Kevin Bru whipping in a fantastic cross and Pitman flashing a header into the net.
Town were inches away from a second soon after, Murphy sending the ball across goal and Pitman just failing to get on the end of it. Murphy was left with space in the box but couldn’t get his shot on goal as Town threatened to take a stranglehold on the game inside the first 10 minutes.
Pitman showed his confidence with an overhead kick from outside the box that drifted just over the bar as Rotherham once again struggled to deal with Gerken’s kick downfield.
Murphy fizzed in another terrific cross that was destined for Pitman until Farrend Rawson got his head on the ball to avert danger, while at the other end Rotherham got their first sight of goal, Matt Derbyshire’s shot at the nearpost deflected wide.
Seconds later Town had struck again, Douglas robbing Green and firing past Camp from 25 yards on 22 minutes. Pitman headed wide from Bru’s cross as Blues looked dangerous at every turn, Barker smashing a shot over as Rotherham searched for a response.
Murphy twisted and turned inside his marker and his deflected shot looked destined for the net until Camp’s right hand intervened, the Millers’ ‘keeper then doing well again to tip over Pitman’s outrageous lob from the angle.
There was no respite for the home side though and from the corner Murphy got the goal his play had deserved, firing in left footed from 12 yards to all but seal the points for Town before the break.
There was still time before the half-time whistle for Murphy to hit the bar after Pitman put him in on goal, Sears smashing the rebound wide.
Rotherham made two changes at the break, Jonson Clarke-Harris on for Green and Richie Smallwood for Tom Thorpe but within two minutes of the restart, Murphy had grabbed his second and Town’s fourth after shrugging off Rawson and finding the bottom corner.
Luke Chambers fired high over the bar after a flowing move but it was the Millers who struck next, a brilliant debut goal from Barker, who was making his first appearance on loan from Manchester City.
Just before the hour, the Millers started to believe they could stage an unbelievable comeback when Derbyshire smashed in a fantastic strike from the angle that gave Gerken no chance.
Clarke-Harris ripped a shot over the bar as Rotherham grew in confidence and attacking threat, Blues making a first change with Maitland-Niles on for Bru midway through the half.
Sears couldn’t find Murphy with the Irishman free on the left, then Murphy was crowded out as Town looked for a fifth. Last season’s top scorer in the Championship would not be denied though and on 72 minutes he completed his hat-trick with a crisp finish from inside the box.
Camp held firm from Pitman, Christophe Berra had a header hacked clear before Sears was given a standing ovation from the 1000 strong Blue Army as he made way for Giles Coke.
The win extends Town’s unbeaten run to four games in what was Blues’ heaviest victory under Mick McCarthy’s command.