Goals from Brett Pitman, Jonathan Douglas and Daryl Murphy - his first of the season - have given the Blues a 3-0 lead at Rotherham at half-time after a dominant first 45 minutes.
Boss Mick McCarthy made one change to his line-up with Ainsley Maitland-Niles, who suffered a foot injury in Tuesday’s 2-0 home win against Bolton, dropping to the bench and Douglas joining Cole Skuse in the middle of midfield with Kevin Bru on the right.
Strike trio Murphy, Pitman and Freddie Sears again all started - Sears in a wide left role - with David McGoldrick, a sub against the Trotters, missing out having been a doubt with a groin problem.
Former Town loanees Danny Collins, Paul Green and Frazer Richardson all began the game for the bottom-of-the-table Millers. Midfielder Brandon Barker, 19, who joined on loan from Manchester City made his senior debut.
Following an impeccably observed minute’s silence ahead of Remembrance Sunday, the Blues almost profited from poor Rotherham defending in the opening minute. The ball broke to Sears inside the Millers’ area on the left from a misdirected headed clearance but the striker’s effort was blocked by keeper Lee Camp.
Town kept up the early pressure and in the fourth minute Sears’s excellent cross from the left was bundled behind ahead of Douglas by Harry Toffolo.
After the corner had been cleared back to Bru on the right, the Mauritius international crossed to Christophe Berra, who nodded back from deep to central defensive partner Tommy Smith but the New Zealand international’s shot on the turn flew over.
But a Town lead wasn’t too long in coming. In the eighth minute, as Rotherham defenders overplayed inside their own area, Sears blocked a clearance which fell to Bru. The midfielder whipped over another cross from the right and Pitman’s flicked header flew across Camp and into the net for his fifth goal of the season and his second in two games.
Having gone in front, the Blues kept up the pressure, Douglas nodding yet another Bru cross down to skipper Luke Chambers, who scuffed his shot.
Town continued their house-on-fire start to the game and in the 16th minute Pitman looped an overhead kick from the edge of the box only just over Camp’s crossbar.
Rotherham briefly threatened in the 22nd minute, Berra getting in ahead of Matt Derbyshire as the former Blackburn man looked to turn a cross home at the near post.
But Town were still on top and a minute later they increased their lead. After Sears had closed down Camp as he looked to clear a long ball on the edge of his area, Douglas dispossessed a ponderous Green midway inside the Millers’ half.
The Irishman took a couple of touches before smashing a low 25-yard shot past the keeper and into the net to claim his first goal for the Blues.
Soon after the second goal, Pitman flicked a header wide then Rotherham debutant Barker shot well over from distance.
On the half hour Camp did well to get down to his right to keep out a deflected strike from Murphy and deny last season’s 27-goal Championship top scorer his first goal of this campaign.
Toffolo picked up the game’s first yellow card in the 40th minute after pulling back Pitman having lost possession to the Town striker on halfway.
Camp tipped over a clever Pitman lob from the right of the area on 43 and from the resultant corner the Blues added to their lead again.
The ball ricocheted around the area following Bru’s corner from the right and eventually fell to Murphy, who hit an effort which was scuffed but still beat Camp to finally end his duck for the season. All Town’s other nine outfield players went over to celebrate with the striker, who will have been delighted and relieved in equal measure.
In first-half injury time the Irish international could have scored again. Pitman’s pass sent him away on the right of the box from where he crashed a shot against Camp’s crossbar. The loose ball fell to Sears on the edge of the area but his strike was too high.
Not long after referee Darren Drysdale blew his whistle to end a brilliant Town first half display and trigger loud boos from the home support, angry at their side’s woeful performance.
Town had seized the initiative from the off and could have been ahead before Pitman’s opener.
Douglas created and scored the second, although like Pitman’s it owed much to Sears’s closing down, and Murphy’s long-awaited but well deserved first of the season was the icing on the cake at the end of the Blues’ 45 minutes of the season.
Rotherham: Camp, Richardson, Rawson, Collins, Toffolo, Thorpe, G Ward, Green, Barker, Derbyshire, D Ward. Subs: Collin, Broadfoot, Buxton, Smallwood, Newell, Clarke-Harris, Andreu.
Town: Gerken, Chambers (c), Smith, Berra, Knudsen, Skuse, Douglas, Bru, Sears, Pitman, Murphy. Subs: Bialkowski, Malarczyk, Parr, Coke, Maitland-Niles, Oar, Touré.