West Ham's first effort was a Teddy Sheringham free kick, but, unlike on Saturday, it went over rather than in.
Both the home debutant centre halves then tried to get in on the act; first, Calum Davenport had a header cleared off the line by Sedgwick and then Malky Mackay, in another well worked corner from Matthew Etherington, headed wide at the near post.
Not to be outdone, Tomas Repka hit a venomous first time strike after Rotherham keeper Michael Pollitt parried a white-boots-wearing Matthew cross from the left; Pollitt blocked.
Luke Chadwick then saw a clever flick go just wide from a low Etherington ball.
The ever-industrious Nigel Reo-Coker was next to have a go, forcing a spilled save from Pollitt from long distance, while Marlon Harewood had a looping header saved following a Carl Fletcher cross.
The second half saw West Ham frustrated, with the first on target shot not coming until midway through - but it was certainly worth the wait.
After Marlon Harewood was fouled by Garner, Etherington stepped up to curl a free kick past Pollitt - to the dismay of his hard-working defenders who included former Hammers Robbie Stockdale, who spent a spell last season on loan from Middlesbrough, and Scott Minto.
To make matters worse for the bottom of the table visitors, Richie Barker was then stretchered off after a robust - but clean - challenge from Davenport; he later was able to limp out of the stadium, however.
It did little to cheer Rotherham's 155 travelling fans who had seen their side battle gamely.
A lively Marlon Harewood had a couple of shots saved as the game became more open with Rotherham now having to be more adventurous, but the Hammers fans had to content themselves with the one goal - and, of course, three hard-earned points.
Malky Mackay replaced Hayden Mullins with Tomas Repka switching to right back, while Chris Powell came in for Rufus Brevett at left back to make his West Ham debut.
TEAM: Bywater, Repka, Fletcher, Sheringham, Harewood, Etherington [Mullins], Reo-Coker, Mackay, Davenport, Chadwick [Rebrov], Powell.
Subs unused: Walker, Brevett, Nowland.
Attendance: 26,233